Content-Type: multipart/mixed; boundary="-------------0305121201415" This is a multi-part message in MIME format. ---------------0305121201415 Content-Type: text/plain; name="03-219.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-219.keywords" Nonequilibrium statistical mechanics, entropy production, heat conduction ---------------0305121201415 Content-Type: application/postscript; name="export.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="export.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: heat.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Bold Times-Roman Times-Italic %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -D 600 -Z -f heat %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.05.06:1636 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. 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Ff(\003)1708 1863 y Fk(+)d Fm(AQ)44 b Fk(=)h Fl(\000)p Fm(B)30 b(;)1380 b Fu(\(1\))0 2085 y(where)975 2225 y Fm(A)44 b Fk(=)1212 2104 y Fg(\022)1290 2165 y Fl(\000)p Fk(\000)100 b Fl(\000)p Fm(V)1331 2285 y Fi(1)191 b(0)1701 2104 y Fg(\023)1803 2225 y Fm(;)216 b(B)50 b Fk(=)2290 2104 y Fg(\022)2368 2165 y Fk(2\000)p Fm(T)113 b Fi(0)2430 2285 y(0)162 b(0)2720 2104 y Fg(\023)2823 2225 y Fm(:)0 2442 y Fu(Here,)28 b Fk(\000)f Fu(and)g Fm(T)41 b Fu(are)28 b(the)f(diagonal)f(matrices)g(whose)h(elements)f(are)i Fk(\000)2508 2457 y Fj(i)2563 2442 y Fu(and)f Fm(T)2791 2457 y Fj(i)2819 2442 y Fu(.)38 b(W)-8 b(e)27 b(denote)g(by)g Fl(H)32 b Fk(=)g Fl(f)p Fm(i)g Fk(:)0 2563 y(\000)61 2578 y Fj(i)130 2563 y Fl(6)p Fk(=)40 b(0)p Fl(g)31 b Fu(the)h(indices)f(of)h(the)f(masses)h(in)f(direct)h(contact)f(with)g (a)h(heat)g(bath.)51 b(The)32 b(follo)n(wing)e(condition)0 2683 y(assures)25 b(uniqueness)e(of)i(the)g(in)l(v)n(ariant)e(measure,) i(and)g(can)g(be)g(easily)f(deri)n(v)o(ed)g(from)h([1])g(:)p Black 0 2907 a Fo(Lemma)g(1)p Black 49 w Fe(Consider)h(the)h(space)g Fl(S)35 b Fe(spanned)26 b(by)h(the)g(vector)o(s)g Fl(f)p Fm(V)2412 2871 y Fj(k)2454 2907 y Fm(e)2499 2922 y Fj(i)2528 2907 y Fm(;)17 b(i)31 b Fl(2)i(H)q Fm(;)17 b(k)34 b Fk(=)e(0)p Fm(;)17 b(:)g(:)g(:)e(;)i(n)p Fl(g)p Fe(,)28 b(wher)l(e)g Fm(e)3797 2922 y Fj(i)0 3027 y Fe(denotes)k(the)h Fm(i)525 2991 y Fq(th)629 3027 y Fe(unit)f(vector)h(of)f Fi(R)1293 2991 y Fj(n)1340 3027 y Fe(.)54 b(If)33 b Fl(S)50 b Fk(=)43 b Fi(R)1826 2991 y Fj(n)1872 3027 y Fe(,)35 b(then)d(\(1\))h(has)g(a)f (unique)g(solution.)53 b(Mor)l(eo)o(ver)-11 b(,)35 b(this)0 3147 y(solution)23 b(is)h(positive)g(de\002nite)o(.)146 3337 y Fu(When)k(the)f(condition)f(of)h(Lemma)g(1)h(is)f(not)f (satis\002ed,)i(a)g(change)g(of)f(coordinates)g(sho)n(ws)f(that)h(at)g (least)0 3457 y(one)33 b(mode)g(is)g(neither)g(coupled)g(to)g(a)h(heat) f(bath)g(nor)g(to)g(the)g(rest)h(of)f(the)g(system.)56 b(The)33 b(simplest)f(e)o(xam-)0 3578 y(ple)d(where)i(this)d(happens)h (is)h(sho)n(wn)e(in)h(Fig.)h(1)f(\(see)h([2,)g(3]\).)45 b(The)30 b(masses)f(1)g(and)h(2)f(are)i(coupled)e(to)g(heat)0 3698 y(baths,)c(while)f(the)h(masses)g(3)g(and)g(4)h(are)f(only)g (coupled)g(to)g(the)g(masses)f(1)h(and)h(2.)31 b(All)25 b(the)g(springs)f(ha)n(v)o(e)h(the)0 3818 y(same)32 b(coupling)e (constant.)51 b(Writing)30 b(the)i(equations)f(of)g(motion,)h(one)g (easily)f(checks)h(that)f(the)h(v)n(ariables)0 3939 y Fm(q)f Fk(=)d Fm(q)221 3954 y Fq(3)283 3939 y Fl(\000)22 b Fm(q)425 3954 y Fq(4)490 3939 y Fu(and)j Fm(p)i Fk(=)h Fm(p)888 3954 y Fq(3)950 3939 y Fl(\000)22 b Fm(p)1098 3954 y Fq(4)1163 3939 y Fu(e)n(v)n(olv)o(e)h(as)i(an)g(isolated)f (harmonic)g(oscillator)-5 b(.)p Black Black Black 1206 4696 a @beginspecial 0 @llx 0 @lly 170 @urx 62 @ury 1694 @rwi @setspecial %%BeginDocument: los1.eps %!PS-Adobe-2.0 %%BoundingBox: 0 0 170 62 %%Title: los1.eps %%Creator: Martin's amazing postscript figure generator %%Pages: 1 %%PageOrder: Ascend %%EndComments /m {moveto} def /rm {rmoveto} def /l {lineto} def /rl {rlineto} def /n {newpath} def /cl {closepath} def /s {stroke} def /srgb {setrgbcolor} def /lw {setlinewidth} def /f {fill} def /it {/Times-Italic findfont} def /ro {/Times-Roman findfont} def /bf {/Times-Bold findfont} def /bi {/Times-BoldItalic findfont} def /sy {/Symbol findfont} def /sc {scalefont} def /sw {stringwidth} def /sf {setfont} def /cp {currentpoint} def /gs {gsave} def /gr {grestore} def /sd {setdash} def /t {show} def /b {-1 -1 rl} def /c {0 -1 rl} def /d {1 -1 rl} def /e {-1 0 rl} def /g {1 0 rl} def /h {-1 1 rl} def /i {0 1 rl} def /j {1 1 rl} def 1 setlinejoin /adict 5 dict def /ato { adict begin /len exch def /py exch def /px exch def cp /opy exch def /opx exch def px py l gs [] 0 sd 0 setlinejoin px py translate px opx ne py opy ne or { py opy sub px opx sub atan rotate n 0 0 m len neg len 3 div rl len 5 div len 3 div neg rl len 5 div neg len 3 div neg rl cl gs f gr s } {0 0 m 0 0 l} ifelse gr end } def /ellipsedict 8 dict def ellipsedict /mtrx matrix put /el { ellipsedict begin /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix end } def 0.12 0.12 scale 4 lw [] 0 sd n 393 286 m i i i i i i i i i i i i i j i i i g i i g i i g i g i g i g i g i g i g i g g i g g i g g g g i g g g g g g g g 419 316 l g g g g 423 315 l g g g 426 314 l g g 428 313 l g g 430 312 l g 431 311 l g 433 310 l g 434 309 l g 435 308 l g 436 307 l g 437 306 l g 438 305 l 438 304 l g 439 303 l g 440 302 l 440 301 l g 441 300 l 441 299 l g 442 298 l 442 297 l 442 296 l 442 295 l 442 294 l 442 293 l 442 292 l 441 292 l 440 292 l 440 291 l 439 291 l i 438 292 l 437 292 l 436 293 l 435 293 l i 434 294 l i 433 295 l i i 432 297 l i i 431 299 l i i 430 301 l i i 429 303 l i i i i 428 307 l i i i i i i i i i i i g i i i i g i i i g i i g i g i i g i g i g i g 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b(of)f(ener)n(gy)g(conserv)n(ation,)f(the)h(total)f(heat)g(\003ux)h(at) g(e)n(v)o(ery)f(point)g(has)h(a)n(v)o(erage)g(zero)g(in)g(the)f(steady) 0 4104 y(state.)51 b(In)32 b(the)f(sequel,)i(we)f(only)f(consider)g(a)n (v)o(erage)h(quantities)e(and)i(by)f Fe(\003ux)h Fu(we)g(al)o(w)o(ays)f (mean)h Fe(aver)o(a)o(g)o(e)0 4225 y(\003ux)25 b(in)f(the)h(steady)f (state)p Fu(.)146 4466 y(V)-11 b(ery)28 b(fe)n(w)f(results)g(are)h(a)n (v)n(ailable)f(concerning)g(the)g Fe(dir)l(ection)f Fu(of)i(the)f(heat) h(\003ux)o(es)f(in)g(the)g(system.)37 b(The)0 4587 y(main)24 b(one)h(is)f(the)h(positi)n(vity)d(of)j(the)f(global)g(entrop)o(y)h (production,)e(namely)1614 4856 y Fl(\000)1714 4773 y Fg(X)1708 4956 y Fj(i)p Ff(2H)1883 4788 y Fm(\036)1941 4803 y Fj(i)p 1883 4832 86 4 v 1883 4924 a Fm(T)1940 4939 y Fj(i)2006 4856 y Fm(>)28 b Fk(0)d Fm(:)0 5147 y Fu(This)35 b(\(strict\))g(inequality)g(has)g(been)h(pro)o(v)o(ed)e (in)i([4])g(for)g(an)f(anharmonic)g(chain)h(between)g(tw)o(o)f(baths)g (at)0 5268 y(dif)n(ferent)c(temperatures.)48 b(Under)31 b(the)g(conditions)e(of)i(Lemma)g(1,)h(one)f(can)g(easily)g(sho)n(w)f (that)g(it)h(remains)0 5388 y(v)n(alid)21 b(for)g(harmonic)h(netw)o (orks)f([2].)29 b(Because)23 b(the)f(matrix)f Fm(Q)h Fu(is)f(positi)n(v)o(e)e(de\002nite,)j(we)g(can)g(also)g(conclude:)p Black Black eop %%Page: 4 4 4 3 bop Black 0 266 a Fo(4)3189 b Fu(H)t Fh(E)t(A)-5 b(T)31 b(FL)t(U)t(X)t(E)t(S)p Black Black 0 573 a Fo(Lemma)25 b(2)p Black 49 w Fe(The)i(point\(s\))f(attac)o(hed)g(to)g(the)h (hottest)f(bath\(s\))g(cannot)g(absorb)g(heat)g(fr)l(om)g(the)h(other)f (baths.)0 693 y(The)f(point\(s\))f(attac)o(hed)g(to)g(the)h(coldest)f (bath\(s\))g(cannot)g(inject)g(heat)h(in)f(the)h(system.)0 884 y(Pr)l(oof)o(.)37 b Fu(If)i(all)f(the)h(temperatures)f(are)i(the)e (same,)k(say)d Fm(#)p Fu(,)j(one)d(easily)f(checks)h(that)f(the)h (steady)f(state)h(is)0 1004 y(Gibbsian,)24 b(that)g(is)1487 1158 y Fm(Q)k Fk(=)f Fm(#)1786 1037 y Fg(\022)1864 1098 y Fi(1)158 b(0)1864 1218 y(0)99 b Fm(V)2098 1182 y Ff(\000)p Fq(1)2209 1037 y Fg(\023)2311 1158 y Fm(:)1371 b Fu(\(4\))0 1370 y(In)30 b(this)e(equilibrium)g(state)h(all)h(the)f(\003ux)o(es)g (v)n(anish)g(and)g(the)h(lemma)f(is)g(tri)n(vially)e(v)o(eri\002ed.)45 b(Consider)30 b(ne)o(xt)0 1490 y(a)g(system)f Fl(S)38 b Fu(with)29 b(at)g(least)h(tw)o(o)f(dif)n(ferent)h(temperatures,)g (and)g(denote)g(by)f Fm(Q)h Fu(the)g(solution)e(to)i(the)f(corre-)0 1610 y(sponding)d(Eq.\(1\).)39 b(Let)27 b Fm(T)926 1625 y Fq(max)1090 1610 y Fu(be)g(the)h(temperature)f(of)h(the)f(hottest)g (heat)g(bath\(s\))h(of)f Fl(S)36 b Fu(and)27 b Fk(\002)33 b Fm(>)g(T)3568 1625 y Fq(max)3731 1610 y Fu(be)0 1731 y(an)e(arbitrary)h(higher)f(temperature.)50 b(W)-8 b(e)31 b(de\002ne)h(a)g(system)e Fl(S)2224 1695 y Ff(0)2279 1731 y Fu(as)i(a)f(cop)o(y)g(of)g Fl(S)40 b Fu(b)n(ut)30 b(whose)h(temperature)0 1851 y(matrix)24 b Fm(T)356 1815 y Ff(0)404 1851 y Fu(is)g(gi)n(v)o(en)g(by)1212 2133 y Fm(T)1283 2092 y Ff(0)1269 2158 y Fj(i)1334 2133 y Fk(=)1437 1987 y Fg(\()1545 2072 y Fk(\002)e Fl(\000)h Fm(T)1800 2087 y Fj(i)1856 2072 y Fm(>)28 b Fk(0)82 b(for)25 b Fm(i)j Fl(2)g(H)e Fm(;)1545 2193 y Fk(0)497 b(otherwise)26 b Fm(:)0 2417 y Fu(Let)i Fm(Q)238 2381 y Ff(0)290 2417 y Fu(be)g(the)g(solution)e(to)h(Eq.\(1\))h(for)h Fl(S)1508 2381 y Ff(0)1532 2417 y Fu(.)40 b(W)-8 b(e)29 b(note)e(that)h(when)g (all)g(the)f(parameters)i(b)n(ut)e Fm(T)42 b Fu(are)29 b(\002x)o(ed)e(in)0 2537 y(Eq.\(1\),)e(the)h(solution)d Fm(Q)p Fu(\()p Fm(T)14 b Fu(\))26 b(is)f(linear)h(in)f Fm(T)14 b Fu(.)33 b(Therefore)26 b Fm(Q)d Fk(+)f Fm(Q)2306 2501 y Ff(0)2356 2537 y Fu(is)j(a)g(Gibbsian)g(matrix)f(\(4\))i(with)f Fm(#)k Fk(=)g(\002)p Fu(,)0 2658 y(in)24 b(particular)1590 2781 y Fm(X)1671 2796 y Fj(ii)1745 2781 y Fk(+)e Fm(X)1932 2740 y Ff(0)1924 2806 y Fj(ii)2004 2781 y Fk(=)27 b(\002)e Fm(;)0 2959 y Fu(where)39 b(we)f(ha)n(v)o(e)g(used)g(the)g(block)g (notation)f(\(2\))i(for)f Fm(Q)h Fu(and)f Fm(Q)2349 2923 y Ff(0)2373 2959 y Fu(.)71 b(Since)39 b(both)e(matrices)h(are)h(positi) n(v)o(e-)0 3079 y(de\002nite,)24 b(we)h(ha)n(v)o(e)f Fm(X)779 3094 y Fj(ii)856 3079 y Fu(and)h Fm(X)1114 3043 y Ff(0)1106 3104 y Fj(ii)1186 3079 y Fm(>)i Fk(0)p Fu(,)e(therefore)g Fm(X)1853 3094 y Fj(ii)1933 3079 y Fm(<)i Fk(\002)e Fu(for)f(an)o(y)g Fk(\002)k Fm(>)f(T)2708 3094 y Fq(max)2844 3079 y Fu(,)e(and)f (\002nally)g Fm(X)3422 3094 y Fj(ii)3502 3079 y Fl(\024)k Fm(T)3664 3094 y Fq(max)3800 3079 y Fu(.)0 3200 y(W)-8 b(e)29 b(consider)f(ne)o(xt)f(the)i(\003ux)f Fm(\036)1115 3215 y Fj(i)1172 3200 y Fu(entering)f(the)i(system)e(through)g(a)i (\223hot\224)f(point)56 b Fm(i)29 b Fu(for)g(which)f Fm(T)3435 3215 y Fj(i)3497 3200 y Fk(=)34 b Fm(T)3664 3215 y Fq(max)3800 3200 y Fu(.)0 3320 y(Because)26 b(of)f(Eq.\(3\))f (we)h(ha)n(v)o(e)985 3543 y Fm(\036)1043 3558 y Fj(i)1099 3543 y Fk(=)j(\000)1264 3558 y Fj(i)1308 3543 y Fu(\()p Fm(T)1398 3558 y Fq(max)1556 3543 y Fl(\000)23 b(h)p Fm(p)1744 3502 y Fq(2)1744 3568 y Fj(i)1783 3543 y Fl(i)p Fu(\))28 b Fk(=)f(\000)2047 3558 y Fj(i)2092 3543 y Fu(\()p Fm(T)2182 3558 y Fq(max)2340 3543 y Fl(\000)c Fm(X)2521 3558 y Fj(ii)2573 3543 y Fu(\))28 b Fl(\025)g Fk(0)c Fm(:)0 3766 y Fu(The)c(corresponding)g(inequality)f(for)h(the)g(cold)g (point\(s\))g(is)g(obtained)f(by)h(an)h(equi)n(v)n(alent)d (construction.)28 b(This)0 3887 y(concludes)c(the)h(proof)g(of)g(the)f (Lemma)g(2.)146 4128 y(The)k(tw)o(o)f(results)f(we)i(ha)n(v)o(e)f (mentioned)g(gi)n(v)o(e)f(some)h(information)e(on)j(ho)n(w)e(the)i (system)e(of)h(oscillators)0 4249 y(e)o(xchanges)c(heat)g(with)f(the)h (baths.)29 b(W)-8 b(e)23 b(are)h(no)n(w)e(interested)h(in)f(kno)n(wing) g(ho)n(w)g(the)h(\003ux)g(propagates)f Fe(within)0 4369 y Fu(the)35 b(system)g(of)h(oscillators.)61 b Fe(The)37 b(main)e(observation)f(of)h(this)g(note)g(is)g(that)g(\223e)o (verything\224)g(is)h(possible)p Fu(,)0 4490 y(basically)28 b(through)f(superposition)g(of)i(elementary)f(solutions.)40 b(Indeed,)30 b(by)e(the)g(linearity)g(of)h Fm(Q)p Fu(\()p Fm(T)14 b Fu(\),)29 b(each)0 4610 y(heat)20 b(bath)g(can)g(be)h (considered)f(as)g(an)g(independent)f(\003ux)h(source,)i(and)e(the)g (total)f(\003ux)h(at)g(an)o(y)g(point)f(is)h(simply)0 4730 y(obtained)j(by)h(adding)f(the)h(contrib)n(ution)e(of)i(all)g(the) g(baths.)30 b(This)23 b(is)h(ho)n(w)f(the)h(four)g(e)o(xamples)e(belo)n (w)i(can)g(be)0 4851 y(found.)p Black 0 5077 a Fo(Example)h(1)p Black 49 w Fu(A)g(linear)f(chain)0 5268 y(Consider)h(a)g(linear)g (chain)g(composed)f(of)h(four)h(equal)e(masses,)h(each)g(of)h(which)e (is)h(coupled)f(to)h(a)g(heat)h(bath.)0 5388 y(In)g(the)f(setup)g(of)h (Fig.)g(2,)g(the)f(heat)h(\003ux)g(is)f(going)g(against)f(the)i (\(local\))g(temperature)f(gradient)h(between)f(the)p Black Black eop %%Page: 5 5 5 4 bop Black 2 266 a Fu(H)t Fh(E)t(A)-5 b(T)32 b(FL)t(U)t(X)t(E)t(S) 3192 b Fo(5)p Black Black Black Black 736 920 a @beginspecial 0 @llx 0 @lly 283 @urx 53 @ury 2824 @rwi @setspecial %%BeginDocument: example1.eps %!PS-Adobe-2.0 %%BoundingBox: 0 0 283 53 %%Title: example1.eps %%Creator: Martin's amazing postscript figure generator %%Pages: 1 %%PageOrder: Ascend %%EndComments /m {moveto} def /rm {rmoveto} def /l {lineto} def /rl {rlineto} def /n {newpath} def /cl {closepath} def /s {stroke} def /srgb {setrgbcolor} def /lw {setlinewidth} def /f {fill} def /it {/Times-Italic findfont} def /ro {/Times-Roman findfont} def /bf {/Times-Bold findfont} def /bi {/Times-BoldItalic findfont} def /sy {/Symbol findfont} def /sc {scalefont} def /sw {stringwidth} def /sf {setfont} def /cp {currentpoint} def /gs {gsave} def /gr {grestore} def /sd {setdash} def /t {show} def /b {-1 -1 rl} def /c {0 -1 rl} def /d {1 -1 rl} def /e {-1 0 rl} def /g {1 0 rl} def /h {-1 1 rl} def /i {0 1 rl} def /j {1 1 rl} def 1 setlinejoin /adict 5 dict def /ato { adict begin /len exch def /py exch def /px exch def cp /opy exch def /opx exch def px py l gs [] 0 sd 0 setlinejoin px py translate px opx ne py opy ne or { py opy sub px opx sub atan rotate n 0 0 m len neg len 3 div rl len 5 div len 3 div neg rl len 5 div neg len 3 div neg rl cl gs f gr s } {0 0 m 0 0 l} ifelse gr end } def /ellipsedict 8 dict def ellipsedict /mtrx matrix put /el { ellipsedict begin /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix end } def 0.12 0.12 scale 4 lw [] 0 sd n 118 47 m 118 283 l s n 826 47 m 826 283 l s n 1535 47 m 1535 283 l s n 2244 47 m 2244 283 l s n 165 47 m 165 46 l 165 45 l g 166 44 l 166 43 l g 167 42 l 168 41 l 168 40 l g 169 39 l g 170 38 l 170 37 l g 171 36 l g 172 35 l g 173 34 l g 174 33 l g g 176 32 l g 177 31 l g g 179 30 l g g 181 29 l g g g 185 28 l g g g g g g g g g g i g g g i g g g i g i g g i g i g j i g j i g i g i g i i g i i g i i g i i i g i i i g i i i i i i i i i i 216 62 l i i 215 64 l i 214 65 l i 213 66 l 213 65 l 212 65 l 211 65 l 211 64 l 211 63 l 210 63 l 210 62 l 210 61 l 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369 29 l g g g 373 28 l g g g g g g g g g g i g g g j g g i g j g i g i g j j g i i g i g i g i i g i j i i g i i g i i i i g i i i i i i i i i i 404 62 l i i 403 64 l i 402 65 l i 401 66 l s 401 66 m 401 65 l 400 65 l 400 64 l 399 64 l 399 63 l 399 62 l 398 62 l 398 61 l 398 60 l 398 59 l 398 58 l 398 57 l 398 56 l 398 55 l 398 54 l 398 53 l 398 52 l 399 51 l 399 50 l 399 49 l 399 48 l g 400 47 l 400 46 l 401 45 l 401 44 l 402 43 l 402 42 l g 403 41 l 403 40 l g 404 39 l g 405 38 l 406 37 l 406 36 l g 407 35 l g 408 34 l g g 410 33 l g 411 32 l g 412 31 l g g 414 30 l g g 416 29 l g g g 420 28 l g g g g g g g g g g i g g g j g g i g j g i g i g j g i g i j i g i g i i g i j i i g i i g i i i i g i i i i i i i i i i 451 62 l i i 450 64 l i 449 65 l i 448 66 l 448 65 l 447 65 l 447 64 l 446 64 l 446 63 l 446 62 l 445 62 l 445 61 l 445 60 l 445 59 l 445 58 l 445 57 l 445 56 l 445 55 l 445 54 l 445 53 l 445 52 l g 446 51 l 446 50 l 446 49 l 446 48 l g 447 47 l 447 46 l 448 45 l 448 44 l 449 43 l 449 42 l g 450 41 l 450 40 l g 451 39 l g 452 38 l 453 37 l 454 36 l 454 35 l g 456 34 l g 457 33 l g 458 32 l g 459 31 l g g 461 30 l g g 463 29 l g g g 467 28 l g g g g g g g g g g i g g g j g g i g j g i g i g j g i g i j i g i g i i g i j i i g i i g i i i i g i i i i i i i i i i 498 62 l i i 497 64 l i 496 65 l i 495 66 l 495 65 l 494 65 l 494 64 l 493 64 l 493 63 l 493 62 l 492 62 l 492 61 l 492 60 l 492 59 l 492 58 l 492 57 l 492 56 l 492 55 l 492 54 l 492 53 l 492 52 l g 493 51 l 493 50 l 493 49 l 493 48 l g 494 47 l 494 46 l g 495 45 l 495 44 l g 496 43 l 496 42 l g 497 41 l 497 40 l g 498 39 l g 499 38 l g 500 37 l 501 36 l 501 35 l g 502 34 l g g 504 33 l g 505 32 l g 507 31 l g 508 30 l g g 511 29 l g g g 514 28 l g g g g g g g g g g i g g g j g g i g j g i g j g i g i g i j i g i g i i g i g i i j i i g i i i j i i i i i i i i i i 545 62 l i i 544 64 l i 543 65 l i 542 66 l 542 65 l 541 65 l 541 64 l 540 64 l 540 63 l 540 62 l 539 62 l 539 61 l 539 60 l 539 59 l 539 58 l 539 57 l 539 56 l 539 55 l 539 54 l 539 53 l 539 52 l g 540 51 l 540 50 l 540 49 l 540 48 l g 541 47 l 541 46 l g 542 45 l 542 44 l g 543 43 l 543 42 l g 544 41 l 544 40 l g 545 39 l g 546 38 l g 547 37 l 548 36 l 549 35 l 550 34 l g 551 33 l g 552 32 l g 554 31 l g 555 30 l g g 558 29 l g g g 561 28 l g g g g g g g g g g j g g g i g g i g g i g i g j g i g i g i j i g i g i i g i j i j i i g i i i j i i i i i i i i i i 592 62 l i i 591 64 l i 590 65 l i 589 66 l 589 65 l 588 65 l 588 64 l 587 64 l 587 63 l 587 62 l 586 62 l 586 61 l 586 60 l 586 59 l 586 58 l 586 57 l 586 56 l 586 55 l 586 54 l 586 53 l 586 52 l g 587 51 l 587 50 l 587 49 l 587 48 l s 587 48 m g 588 47 l 588 46 l g 589 45 l 589 44 l g 590 43 l 590 42 l g 591 41 l 591 40 l g 592 39 l g 593 38 l g 594 37 l 594 36 l g 596 35 l 597 34 l g 598 33 l g 599 32 l g 601 31 l g 602 30 l g g 605 29 l g g g 608 28 l g g g g g g g g g g j g g g i g g i g g i g i g i g g i g i g i j i g i g i j i j i g i i i g i i i g i i i i i i i i i i i 639 63 l i 638 65 l 637 65 l i 636 66 l 636 65 l 635 65 l 635 64 l 634 64 l 634 63 l 634 62 l 633 62 l 633 61 l 633 60 l 633 59 l 633 58 l 633 57 l 633 56 l 633 55 l 633 54 l 633 53 l 633 52 l g 634 51 l 634 50 l 634 49 l 634 48 l g 635 47 l 635 46 l g 636 45 l 636 44 l g 637 43 l 637 42 l g 638 41 l 638 40 l g 639 39 l g 640 38 l g 641 37 l 642 36 l 642 35 l g 644 34 l g 645 33 l g 646 32 l g g 648 31 l g 649 30 l g g g 652 29 l g g g 655 28 l g g g g g g g g g g j g g g i g g i g g i g i g i g g i g i g i j i g i g i i g i g i i g i i i g i i i g i i i i i i i i i i i i 686 63 l i 685 65 l 684 65 l i 683 66 l 683 65 l 682 65 l 682 64 l 681 64 l 681 63 l 681 62 l 680 62 l 680 61 l 680 60 l 680 59 l 680 58 l 680 57 l 680 56 l 680 55 l 680 54 l 680 53 l 680 52 l g 681 51 l 681 50 l 681 49 l 682 48 l 682 47 l 682 46 l g 683 45 l 683 44 l g 684 43 l 684 42 l g 685 41 l 685 40 l g 686 39 l g 687 38 l g 688 37 l 689 36 l 690 35 l g 691 34 l g 692 33 l g 693 32 l g g 695 31 l g 696 30 l g g g 699 29 l g g g 702 28 l g g g g g g g g g g g i g g g i g g i g g i g i g j g i g i g i g i i g i g i i g i g i i g i i i g i i i g i i i i i i i i i i i i 733 63 l i i 732 65 l 731 65 l i 730 66 l 730 65 l 729 65 l 729 64 l 728 64 l 728 63 l 728 62 l 727 62 l 727 61 l 727 60 l 727 59 l 727 58 l 727 57 l 727 56 l 727 55 l 727 54 l 727 53 l 727 52 l g 728 51 l 728 50 l 728 49 l 729 48 l 729 47 l 729 46 l g 730 45 l 730 44 l g 731 43 l 731 42 l g 732 41 l 732 40 l g 733 39 l g 734 38 l g 735 37 l g 736 36 l 737 35 l g 738 34 l g 739 33 l g 740 32 l g g 742 31 l g 743 30 l g g 746 29 l g g g 749 28 l g g g g g g g g g g j g g g i g g i g g i g i g j g i g i g i g i i g i g i j i g i i g i i s n 874 47 m 874 46 l 874 45 l g 875 44 l 875 43 l g 876 42 l 876 41 l g 877 40 l g 878 39 l 878 38 l g 879 37 l g 880 36 l g 881 35 l g 882 34 l g 883 33 l g 885 32 l g 886 31 l g g 888 30 l g g 890 29 l g g g 893 28 l g g g g g g g g g g g i g g g i g g i g g i g g i g i g i g i g i g i g i g i i g i g i i g i i j i i g i i i i i g i i i i i i i 925 61 l i i i 924 64 l i 923 65 l i 922 66 l 921 66 l 921 65 l 920 65 l 920 64 l 920 63 l 919 63 l 919 62 l 919 61 l 919 60 l 919 59 l 918 59 l 918 58 l 918 57 l 918 56 l g 919 55 l 919 54 l 919 53 l 919 52 l 919 51 l 919 50 l g 920 49 l 920 48 l 920 47 l g 921 46 l 921 45 l g 922 44 l 922 43 l g 923 42 l 923 41 l g 924 40 l g 925 39 l 925 38 l g 926 37 l g 927 36 l g 928 35 l g 929 34 l g 930 33 l g 932 32 l g 933 31 l g g 935 30 l g g 937 29 l g g g 940 28 l g g g g g g g g g g g i g g g i g g j g i g g i g i g i g i g i g i g i g i i g i g i i g i i g i i i g i i i i i g i i i i i i i 972 61 l i i i 971 64 l i 970 65 l i 969 66 l 968 66 l 968 65 l 967 65 l 967 64 l 967 63 l 966 63 l 966 62 l 966 61 l 966 60 l 966 59 l 966 58 l 965 58 l 965 57 l g 966 56 l 966 55 l 966 54 l 966 53 l 966 52 l 966 51 l 966 50 l g 967 49 l 967 48 l 967 47 l g 968 46 l 968 45 l g 969 44 l 969 43 l g 970 42 l 970 41 l g 971 40 l g 972 39 l 972 38 l g 973 37 l g 974 36 l g 975 35 l g 976 34 l g 977 33 l g g 979 32 l g 980 31 l g g 982 30 l g g 984 29 l g g g 987 28 l g g g g g g g g g g g i g g g i g g j g i g g i g i g i g i g i g i g i g i i g i g i i g i i g i i i g i i i i j i i i i i i i 1019 61 l i i i 1018 64 l i 1017 65 l i 1016 66 l 1015 66 l 1015 65 l 1014 65 l 1014 64 l 1014 63 l 1013 63 l 1013 62 l 1013 61 l 1013 60 l 1013 59 l 1013 58 l 1013 57 l 1013 56 l 1013 55 l 1013 54 l 1013 53 l 1013 52 l 1013 51 l 1013 50 l g 1014 49 l 1014 48 l 1014 47 l g 1015 46 l 1015 45 l g 1016 44 l 1016 43 l g 1017 42 l 1017 41 l g 1018 40 l g 1019 39 l 1019 38 l g 1020 37 l g 1021 36 l g 1022 35 l g 1023 34 l g 1024 33 l g g 1026 32 l g 1027 31 l g g 1029 30 l g g 1031 29 l g g g 1034 28 l g g g g g g g g g g g i g g g i g g j g i g g i g i g i g i g i g i g i g i i g i g i i g i i g i i i g i i i i g i i i i i i i i 1066 61 l i i i 1065 64 l i 1064 65 l i 1063 66 l 1062 66 l 1062 65 l 1061 65 l 1061 64 l 1061 63 l 1060 63 l 1060 62 l 1060 61 l 1060 60 l 1060 59 l 1060 58 l 1060 57 l 1060 56 l 1060 55 l 1060 54 l 1060 53 l 1060 52 l 1060 51 l 1061 50 l 1061 49 l 1061 48 l 1061 47 l g 1062 46 l 1062 45 l g 1063 44 l 1063 43 l g 1064 42 l 1064 41 l g 1065 40 l g 1066 39 l 1066 38 l g 1067 37 l g 1068 36 l g 1069 35 l g 1070 34 l g 1071 33 l g g 1073 32 l g 1074 31 l g g 1076 30 l g g 1078 29 l g g g 1081 28 l s 1081 28 m g g g g g g g g g g g i g g g i g g j g i g g i g i g i g i g i g i g i g i i g i g i i g i i g i i i g i i i i g i i i i i i i i 1113 61 l i i i 1112 64 l i 1111 65 l i 1110 66 l 1109 65 l 1108 65 l 1108 64 l 1108 63 l 1107 63 l 1107 62 l 1107 61 l 1107 60 l 1107 59 l 1107 58 l 1107 57 l 1107 56 l 1107 55 l 1107 54 l 1107 53 l 1107 52 l 1107 51 l 1108 50 l 1108 49 l 1108 48 l 1109 47 l 1109 46 l 1109 45 l g 1110 44 l 1110 43 l g 1111 42 l 1111 41 l g 1112 40 l g 1113 39 l 1113 38 l g 1114 37 l g 1115 36 l g 1116 35 l g 1117 34 l g 1118 33 l g g 1120 32 l g 1121 31 l g g 1123 30 l g g 1125 29 l g g g 1128 28 l g g g g g g g g g g g i g g g i g g j g i g g i g i g i g i g i g i g i g i j i g i i g i i g i i i g i i i i g i i i i i i i i 1160 61 l i i i 1159 64 l i 1158 65 l i 1157 66 l 1156 65 l 1155 65 l 1155 64 l 1155 63 l 1154 63 l 1154 62 l 1154 61 l 1154 60 l 1154 59 l 1154 58 l 1154 57 l 1154 56 l 1154 55 l 1154 54 l 1154 53 l 1154 52 l 1154 51 l g 1155 50 l 1155 49 l 1155 48 l 1156 47 l 1156 46 l 1156 45 l g 1157 44 l 1157 43 l g 1158 42 l 1158 41 l g 1159 40 l g 1160 39 l 1160 38 l g 1161 37 l g 1162 36 l g 1163 35 l g 1164 34 l g 1165 33 l g g 1167 32 l g 1168 31 l g g 1170 30 l g g 1172 29 l g g g 1175 28 l g g g g g g g g g g g i g g g i g g j g i g g i g i g i g i g i g i g i g i j i g i i g i i g i i i g i i i i g i i i i i i i i 1207 61 l i i i 1206 64 l i 1205 65 l i 1204 66 l 1204 65 l 1203 65 l 1202 65 l 1202 64 l 1202 63 l 1201 63 l 1201 62 l 1201 61 l 1201 60 l 1201 59 l 1201 58 l 1201 57 l 1201 56 l 1201 55 l 1201 54 l 1201 53 l 1201 52 l 1201 51 l g 1202 50 l 1202 49 l 1202 48 l 1203 47 l 1203 46 l 1203 45 l g 1204 44 l 1204 43 l g 1205 42 l 1206 41 l 1206 40 l g 1207 39 l 1208 38 l 1208 37 l g 1209 36 l g 1210 35 l g 1211 34 l g 1213 33 l g 1214 32 l g 1215 31 l g g 1217 30 l g g 1219 29 l g g g 1222 28 l g g g g g g g g g g g i g g g i g g j g i g g i g i g i g i g i g i g i g i j i g i i g i i g i i i g i i i i g i i i i i i i i 1254 62 l i i 1253 64 l i 1252 65 l i 1251 66 l 1251 65 l 1250 65 l 1249 65 l 1249 64 l 1249 63 l 1248 63 l 1248 62 l 1248 61 l 1248 60 l 1248 59 l 1248 58 l 1248 57 l 1248 56 l 1248 55 l 1248 54 l 1248 53 l 1248 52 l 1248 51 l g 1249 50 l 1249 49 l 1249 48 l g 1250 47 l 1250 46 l 1250 45 l g 1251 44 l 1251 43 l g 1252 42 l 1252 41 l g 1253 40 l g 1254 39 l 1255 38 l 1255 37 l g 1256 36 l g 1257 35 l g 1258 34 l g 1259 33 l g g 1261 32 l g 1262 31 l g g 1264 30 l g g 1266 29 l g g g 1269 28 l g g g g g g g g g g g i g g g i g g g i g i g g i g i g i g i g i g i g i g i g i i g i i g i i g i i i g i i i i g i i i i i i i i i 1301 62 l i i 1300 64 l i 1299 65 l i 1298 66 l 1298 65 l 1297 65 l 1296 65 l 1296 64 l 1296 63 l 1295 63 l 1295 62 l 1295 61 l 1295 60 l 1295 59 l 1295 58 l 1295 57 l 1295 56 l 1295 55 l 1295 54 l 1295 53 l 1295 52 l 1295 51 l g 1296 50 l s 1296 50 m 1296 49 l 1296 48 l 1297 47 l 1297 46 l 1297 45 l g 1298 44 l 1298 43 l g 1299 42 l 1299 41 l g 1300 40 l g 1301 39 l 1302 38 l 1302 37 l g 1303 36 l g 1304 35 l g 1305 34 l g 1306 33 l g g 1308 32 l g 1309 31 l g g 1311 30 l g g 1313 29 l g g g 1317 28 l g g g g g g g g g g i g g g i g g g i g i g g i g i g i g i g i g i g i g i j i g i i g i i g i i i g i i i j i i i i i i i i i 1348 62 l i i 1347 64 l i 1346 65 l i 1345 66 l 1345 65 l 1344 65 l 1343 65 l 1343 64 l 1343 63 l 1342 63 l 1342 62 l 1342 61 l 1342 60 l 1342 59 l 1342 58 l 1342 57 l 1342 56 l 1342 55 l 1342 54 l 1342 53 l 1342 52 l 1342 51 l g 1343 50 l 1343 49 l 1343 48 l g 1344 47 l 1344 46 l 1344 45 l g 1345 44 l 1345 43 l g 1346 42 l 1347 41 l 1347 40 l g 1348 39 l g 1349 38 l 1349 37 l g 1350 36 l g 1351 35 l g 1352 34 l g 1354 33 l g 1355 32 l g 1356 31 l g g 1358 30 l g g 1360 29 l g g g 1364 28 l g g g g g g g g g g i g g g i g g j g i g g i g i g i g j i g i g i g i j i g i i g i i g i i i g i i i g i i i i i i i i i i 1395 62 l i i 1394 64 l i 1393 65 l i 1392 66 l 1392 65 l 1391 65 l 1390 65 l 1390 64 l 1390 63 l 1389 63 l 1389 62 l 1389 61 l 1389 60 l 1389 59 l 1389 58 l 1389 57 l 1389 56 l 1389 55 l 1389 54 l 1389 53 l 1389 52 l 1389 51 l g 1390 50 l 1390 49 l 1390 48 l g 1391 47 l 1391 46 l 1391 45 l g 1392 44 l 1392 43 l g 1393 42 l 1394 41 l 1394 40 l g 1395 39 l g 1396 38 l 1396 37 l g 1397 36 l g 1398 35 l g 1399 34 l g 1401 33 l g 1402 32 l g 1403 31 l g g 1405 30 l g g 1407 29 l g g g 1411 28 l g g g g g g g g g g i g g g j g g i g j g i g i g i g j i g i g i g i g i i g i i g i i g i i j i i i g i i i i i i i i i i 1442 62 l i i 1441 64 l i 1440 65 l i 1439 66 l 1439 65 l 1438 65 l 1437 65 l 1437 64 l 1437 63 l 1436 63 l 1436 62 l 1436 61 l 1436 60 l 1436 59 l 1436 58 l 1436 57 l 1436 56 l 1436 55 l 1436 54 l 1436 53 l 1436 52 l 1436 51 l g 1437 50 l 1437 49 l 1437 48 l g 1438 47 l 1438 46 l 1438 45 l g 1439 44 l 1439 43 l g 1440 42 l 1441 41 l 1441 40 l g 1442 39 l g 1443 38 l 1443 37 l g 1444 36 l g 1445 35 l g 1446 34 l g 1448 33 l g 1449 32 l g 1450 31 l g g 1452 30 l g g 1454 29 l g g g 1458 28 l g g g g g g g g g g i g g g j g g i g i g g i g i g i g j j i g i g i g i i g i i g i i g i s n 1582 47 m 1582 46 l g 1583 45 l 1583 44 l g 1584 43 l 1584 42 l g 1585 41 l g 1586 40 l 1586 39 l g 1587 38 l g 1588 37 l g 1589 36 l g 1590 35 l g 1591 34 l g 1592 33 l g 1593 32 l g g 1595 31 l g 1597 30 l g g 1599 29 l g g g 1602 28 l g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i i g i g i i g i i g i i g i i i g i i i i i i g i i 1634 59 l i i i i 1633 63 l i i 1632 65 l i 1631 66 l 1630 66 l 1630 65 l 1629 65 l 1629 64 l 1628 64 l 1628 63 l 1628 62 l 1628 61 l 1627 61 l 1627 60 l 1627 59 l 1627 58 l 1627 57 l 1627 56 l 1627 55 l 1627 54 l g 1628 53 l 1628 52 l 1628 51 l 1628 50 l 1628 49 l g 1629 48 l 1629 47 l 1630 46 l 1630 45 l 1630 44 l g 1631 43 l 1631 42 l g 1632 41 l g 1633 40 l 1633 39 l g 1634 38 l g 1635 37 l g 1636 36 l g 1637 35 l g 1638 34 l g 1639 33 l g 1640 32 l g g 1642 31 l g g 1644 30 l g g 1646 29 l g g g 1649 28 l g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i i g i g i i g i i g i i g i i i g i i i i i i g i i i 1681 59 l i i i i 1680 63 l i i 1679 65 l i 1678 66 l 1677 66 l 1677 65 l 1676 65 l 1676 64 l 1675 64 l 1675 63 l 1675 62 l 1675 61 l 1674 61 l 1674 60 l 1674 59 l 1674 58 l 1674 57 l 1674 56 l 1674 55 l 1674 54 l g 1675 53 l 1675 52 l 1675 51 l 1675 50 l 1675 49 l g 1676 48 l 1676 47 l 1677 46 l 1677 45 l 1677 44 l g 1678 43 l 1678 42 l g 1679 41 l g 1680 40 l 1680 39 l g 1681 38 l g 1682 37 l g 1683 36 l g 1684 35 l g 1685 34 l g 1686 33 l g 1687 32 l g g 1689 31 l g g 1691 30 l g g 1693 29 l g g g 1696 28 l g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i i g i g i i g i i g i i g i i i g i i i i i i g i i i 1728 59 l i i i i 1727 63 l i i 1726 65 l i 1725 66 l 1724 66 l 1724 65 l 1723 65 l 1723 64 l 1722 64 l 1722 63 l 1722 62 l 1722 61 l 1721 60 l 1721 59 l 1721 58 l 1721 57 l 1721 56 l 1721 55 l 1721 54 l g 1722 53 l 1722 52 l 1722 51 l 1722 50 l 1723 49 l 1723 48 l 1723 47 l g 1724 46 l 1724 45 l 1724 44 l g 1725 43 l 1725 42 l g 1726 41 l g 1727 40 l 1727 39 l g 1728 38 l g 1729 37 l g 1730 36 l g 1731 35 l g 1732 34 l g 1733 33 l g 1734 32 l g g 1736 31 l g g 1738 30 l g g 1740 29 l g g g 1743 28 l g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i i g i g i i g i i g i i g i i i g i i i i i g i i i i 1775 59 l i i i i 1774 63 l i i 1773 65 l i 1772 66 l 1771 66 l 1771 65 l 1770 65 l 1770 64 l 1769 64 l 1769 63 l 1769 62 l 1769 61 l 1769 60 l 1768 60 l 1768 59 l 1768 58 l 1768 57 l 1768 56 l 1768 55 l 1768 54 l g 1769 53 l 1769 52 l 1769 51 l 1769 50 l 1770 49 l 1770 48 l 1770 47 l g 1771 46 l 1771 45 l 1772 44 l 1772 43 l 1773 42 l 1773 41 l g 1774 40 l 1775 39 l 1775 38 l g 1776 37 l g 1777 36 l g 1778 35 l g 1779 34 l g 1780 33 l g 1781 32 l g g 1783 31 l g g 1785 30 l g g 1787 29 l s 1787 29 m g g g 1790 28 l g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i i g i g i i g i i g i i g i i i g i i i i i g i i i i i 1822 60 l i i i 1821 64 l i 1820 65 l i 1819 66 l 1818 66 l 1818 65 l 1817 65 l 1817 64 l 1816 64 l 1816 63 l 1816 62 l 1816 61 l 1816 60 l 1815 60 l 1815 59 l 1815 58 l 1815 57 l 1815 56 l 1815 55 l 1816 54 l 1816 53 l 1816 52 l 1816 51 l 1816 50 l g 1817 49 l 1817 48 l 1817 47 l g 1818 46 l 1818 45 l 1819 44 l 1819 43 l g 1820 42 l 1820 41 l g 1821 40 l 1822 39 l 1822 38 l g 1823 37 l g 1824 36 l g 1825 35 l g 1826 34 l g 1827 33 l g 1828 32 l g g 1830 31 l g g 1832 30 l g g 1834 29 l g g g 1837 28 l g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i j i g i i g i j i i g i i i g i i i i i g i i i i i 1869 60 l i i i i 1868 64 l i 1867 65 l i 1866 66 l 1865 66 l 1865 65 l 1864 65 l 1864 64 l 1863 64 l 1863 63 l 1863 62 l 1863 61 l 1863 60 l 1862 60 l 1862 59 l 1862 58 l 1862 57 l 1862 56 l 1862 55 l g 1863 54 l 1863 53 l 1863 52 l 1863 51 l 1863 50 l g 1864 49 l 1864 48 l 1864 47 l g 1865 46 l 1865 45 l 1866 44 l 1866 43 l g 1867 42 l 1867 41 l g 1868 40 l 1869 39 l 1869 38 l g 1870 37 l g 1871 36 l g 1872 35 l g 1873 34 l g 1874 33 l g 1876 32 l g 1877 31 l g g 1879 30 l g g 1881 29 l g g g 1884 28 l g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i g i i g i i g i j i i g i i i g i i i i i g i i i i i 1916 60 l i i i i 1915 64 l i 1914 65 l i 1913 66 l 1912 66 l 1912 65 l 1911 65 l 1911 64 l 1910 63 l 1910 62 l 1910 61 l 1910 60 l 1909 60 l 1909 59 l 1909 58 l 1909 57 l 1909 56 l 1909 55 l g 1910 54 l 1910 53 l 1910 52 l 1910 51 l 1910 50 l g 1911 49 l 1911 48 l 1911 47 l g 1912 46 l 1912 45 l 1913 44 l 1913 43 l g 1914 42 l 1914 41 l g 1915 40 l 1916 39 l 1916 38 l g 1917 37 l g 1918 36 l g 1919 35 l g 1920 34 l g 1921 33 l g 1922 32 l g g 1924 31 l g g 1926 30 l g g 1928 29 l g g g 1931 28 l g g g g g g g g g g g i g g g i g g i g g i g g i g i g i g i g i g i g i g i i g i j i j i i g i i i g i i i i j i i i i i 1963 60 l i i i i 1962 64 l i 1961 65 l i 1960 66 l 1959 66 l 1959 65 l 1958 65 l 1958 64 l 1957 63 l 1957 62 l 1957 61 l 1957 60 l 1956 60 l 1956 59 l 1956 58 l 1956 57 l 1956 56 l 1956 55 l g 1957 54 l 1957 53 l 1957 52 l 1957 51 l 1957 50 l g 1958 49 l 1958 48 l 1958 47 l g 1959 46 l 1959 45 l g 1960 44 l 1960 43 l g 1961 42 l 1961 41 l g 1962 40 l g 1963 39 l 1963 38 l g 1964 37 l g 1965 36 l g 1966 35 l g 1967 34 l g 1968 33 l g 1970 32 l g 1971 31 l g g 1973 30 l g g 1975 29 l g g g 1978 28 l g g g g g g g g g g g i g g g i g g i g g i g g i g i g i g i g i g i g i j i g i j i j i i g i i j i i i i g i i i i i i 2010 60 l i i i i 2009 64 l i 2008 65 l i 2007 66 l 2006 66 l 2006 65 l 2005 65 l 2005 64 l 2005 63 l 2004 63 l 2004 62 l 2004 61 l 2004 60 l 2004 59 l 2003 59 l 2003 58 l 2003 57 l 2003 56 l s 2003 56 m 2003 55 l g 2004 54 l 2004 53 l 2004 52 l 2004 51 l 2004 50 l g 2005 49 l 2005 48 l 2005 47 l g 2006 46 l 2006 45 l g 2007 44 l 2007 43 l g 2008 42 l 2008 41 l g 2009 40 l g 2010 39 l 2010 38 l g 2011 37 l g 2012 36 l g 2013 35 l g 2014 34 l g 2015 33 l g 2017 32 l g 2018 31 l g g 2020 30 l g g 2022 29 l g g g 2025 28 l g g g g g g g g g g g i g g g i g g i g g i g g i g i g i g i g i g i g i g i i g i j i g i i j i i j i i i i g i i i i i i 2057 61 l i i i 2056 64 l i 2055 65 l i 2054 66 l 2053 66 l 2053 65 l 2052 65 l 2052 64 l 2052 63 l 2051 63 l 2051 62 l 2051 61 l 2051 60 l 2051 59 l 2050 59 l 2050 58 l 2050 57 l 2050 56 l g 2051 55 l 2051 54 l 2051 53 l 2051 52 l 2051 51 l 2051 50 l g 2052 49 l 2052 48 l 2052 47 l g 2053 46 l 2053 45 l g 2054 44 l 2054 43 l g 2055 42 l 2055 41 l g 2056 40 l 2057 39 l 2057 38 l g 2058 37 l g 2059 36 l g 2060 35 l g 2061 34 l g 2062 33 l g 2064 32 l g 2065 31 l g g 2067 30 l g g 2069 29 l g g g 2072 28 l g g g g g g g g g g g i g g g i g g i g g i g g i g i g i g i g i g i g i g i i g i j i g i i j i i g i i i i i g i i i i i i i 2104 61 l i i i 2103 64 l i 2102 65 l i 2101 66 l 2100 66 l 2100 65 l 2099 65 l 2099 64 l 2099 63 l 2098 63 l 2098 62 l 2098 61 l 2098 60 l 2098 59 l 2097 59 l 2097 58 l 2097 57 l 2097 56 l g 2098 55 l 2098 54 l 2098 53 l 2098 52 l 2098 51 l 2098 50 l g 2099 49 l 2099 48 l 2099 47 l g 2100 46 l 2100 45 l g 2101 44 l 2101 43 l g 2102 42 l 2102 41 l g 2103 40 l g 2104 39 l 2104 38 l g 2105 37 l g 2106 36 l g 2107 35 l g 2108 34 l g 2109 33 l g g 2111 32 l g 2112 31 l g g 2114 30 l g g 2116 29 l g g g 2119 28 l g g g g g g g g g g g i g g g i g g i g g i g g i g i g i g i g i g i g i g i i g i g i i g i i j i i g i i i i i g i i i i i i i 2151 61 l i i i 2150 64 l i 2149 65 l i 2148 66 l 2147 66 l 2147 65 l 2146 65 l 2146 64 l 2146 63 l 2145 63 l 2145 62 l 2145 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(local)h(temperature)f(with)g(the)g(heat)h(bath,)h(we)e(can)h(also)f (use)0 1760 y(the)g(local)g(kinetic)g(ener)n(gy)g Fl(h)p Fm(p)1073 1724 y Fq(2)1073 1784 y Fj(i)1113 1760 y Fl(i)p Fu(.)52 b(Ho)n(we)n(v)o(er)l(,)33 b(we)g(\002nd)f Fl(h)p Fm(p)2067 1724 y Fq(2)2067 1784 y(2)2106 1760 y Fl(i)42 b Fk(=)f(14)g Fm(<)g Fk(18)h(=)f Fl(h)p Fm(p)2905 1724 y Fq(2)2905 1784 y(3)2944 1760 y Fl(i)p Fu(,)34 b(thus)d(the)i (\223backw)o(ard)0 1880 y(\003ux\224)e(persists.)46 b(This)30 b(\002rst)g(e)o(xample)g(can)h(be)f(easily)g(understood:)41 b(as)30 b(noted)g(in)g(the)h(proof)f(of)g(Lemma)g(2,)0 2001 y(the)24 b(matrix)g Fm(Q)g Fu(solving)f(\(1\))h(is)g(a)h(linear)f (function)f(of)i Fm(T)38 b Fu(and)24 b(so)g(are)h(the)f(\003ux)o(es.)30 b(Thus,)24 b(we)g(can)h(decompose)0 2121 y(our)30 b(system)g(as)g(the)h (sum)f(of)g(tw)o(o)g(similar)g(chains,)h(one)g(with)e(temperatures)i (\()p Fk(100)p Fm(;)17 b Fk(0)p Fm(;)g Fk(0)p Fm(;)g Fk(2)p Fu(\))28 b(and)j(the)f(other)0 2241 y(with)c(\()p Fk(0)p Fm(;)17 b Fk(2)p Fm(;)g Fk(20)p Fm(;)g Fk(0)p Fu(\).)37 b(The)27 b(total)f(\003ux)i(in)e(the)h(middle)f(spring)h (still)f(goes)g(to)h(the)g(right,)g(since)g(temperature)g Fm(T)3785 2256 y Fq(1)0 2362 y Fu(pushes)d(much)g(more)h(ener)n(gy)g (into)f(the)h(chain)f(than)h Fm(T)1887 2377 y Fq(3)1951 2362 y Fu(does.)p Black 0 2608 a Fo(Example)g(2)p Black 49 w Fu(Circulation)f(of)h(heat)p Black Black Black 1089 3500 a @beginspecial 0 @llx 0 @lly 198 @urx 79 @ury 1977 @rwi @setspecial %%BeginDocument: example2.eps %!PS-Adobe-2.0 %%BoundingBox: 0 0 198 79 %%Title: example2.eps %%Creator: Martin's amazing postscript figure generator %%Pages: 1 %%PageOrder: Ascend %%EndComments /m {moveto} def /rm {rmoveto} def /l {lineto} def /rl {rlineto} def /n {newpath} def /cl {closepath} def /s {stroke} def /srgb {setrgbcolor} def /lw {setlinewidth} def /f {fill} def /it {/Times-Italic findfont} def /ro {/Times-Roman findfont} def /bf {/Times-Bold findfont} def /bi {/Times-BoldItalic findfont} def /sy {/Symbol findfont} def /sc {scalefont} def /sw {stringwidth} def /sf {setfont} def /cp {currentpoint} def /gs {gsave} def /gr {grestore} def /sd {setdash} def /t {show} def /b {-1 -1 rl} def /c {0 -1 rl} def /d {1 -1 rl} def /e {-1 0 rl} def /g {1 0 rl} def /h {-1 1 rl} def /i {0 1 rl} def /j {1 1 rl} def 1 setlinejoin /adict 5 dict def /ato { adict begin /len exch def /py exch def /px exch def cp /opy exch def /opx exch def px py l gs [] 0 sd 0 setlinejoin px py translate px opx ne py opy ne or { py opy sub px opx sub atan rotate n 0 0 m len neg len 3 div rl len 5 div len 3 div neg rl len 5 div neg len 3 div neg rl cl gs f gr s } {0 0 m 0 0 l} ifelse gr end } def /ellipsedict 8 dict def ellipsedict /mtrx matrix put /el { ellipsedict begin /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix end } def 0.12 0.12 scale 4 lw [] 0 sd n 283 94 m 283 93 l g 284 92 l g 285 91 l g 286 90 l g 287 89 l 288 88 l 289 87 l 290 86 l g 291 85 l g 292 84 l g 293 83 l g g 295 82 l g 296 81 l g g 298 80 l g 300 79 l g g 302 78 l g g 304 77 l g g g 307 76 l g g g g g 312 75 l g g g g g g g g g g g i g g g g g i g g g i g g i g g i g g i g g i g i g g i g i g i g i g i g i g i g i g i g i j i g i j i g i i g i i g i i g i i i g i i i i g i i 360 112 l 360 111 l 360 110 l 361 109 l 361 108 l 361 107 l 361 106 l g 362 105 l 362 104 l 363 103 l 363 102 l 363 101 l g 364 100 l 364 99 l g 365 98 l g 366 97 l 366 96 l g 367 95 l 368 94 l 368 93 l g 369 92 l g 370 91 l 371 90 l 372 89 l 372 88 l g 373 87 l g 374 86 l g 376 85 l g 377 84 l g 378 83 l g 380 82 l g 381 81 l g 383 80 l g 384 79 l g g 387 78 l g g 389 77 l g g g 392 76 l g g g g g 397 75 l g g g g g g g g g g g i g g g g j g g j g g i g g i g g i g j g i g j g i g i g i g i g i g i g i g i j i g i g i i g i g i i g i i g i i i g i i i g i i i i g i 445 112 l 445 111 l 445 110 l 445 109 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j g g g g i g g g i g g g i g g i g g i g i g g i g i g i g g i g i g i g i g i g i j i g i g i i g i g i i g i i g i i g i i i g i i i g i i i i 614 112 l g 615 111 l 615 110 l 615 109 l 615 108 l 616 107 l 616 106 l 616 105 l g 617 104 l 617 103 l 617 102 l g 618 101 l 618 100 l g 619 99 l 619 98 l g 620 97 l g 621 96 l 621 95 l g 622 94 l g 623 93 l 624 92 l 624 91 l g 625 90 l g 626 89 l g 627 88 l g 628 87 l g 629 86 l g 630 85 l g 631 84 l g 633 83 l g 634 82 l g 636 81 l g 637 80 l g g 639 79 l g g 641 78 l g g 644 77 l g g 647 76 l g g g g 651 75 l g g g g g g g g g g g i g g g g g i g g g i g g j g j g i g g i g j g i g i g i g g i g i g i j i g i g i g i j i g i i g i g i i g i i j i i g i i i i g i i i 699 112 l 699 111 l g 700 110 l 700 109 l 700 108 l 700 107 l g 701 106 l 701 105 l 701 104 l g 702 103 l 702 102 l g 703 101 l 703 100 l g 704 99 l 704 98 l g 705 97 l 706 96 l 706 95 l g 707 94 l 708 93 l 708 92 l g 709 91 l g 710 90 l g 711 89 l g 712 88 l g 713 87 l g 714 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g i g i g i g i g i i g i g i j i g i i g i i g i i g i i g i i i g i i i i i g 1039 112 l 1039 111 l 1039 110 l 1039 109 l 1039 108 l g 1040 107 l 1040 106 l 1040 105 l g 1041 104 l 1041 103 l 1042 102 l 1042 101 l 1043 100 l 1043 99 l g 1044 98 l 1044 97 l g 1045 96 l 1045 95 l g 1046 94 l g 1047 93 l g 1048 92 l 1048 91 l g 1049 90 l g 1050 89 l g 1051 88 l g 1052 87 l g 1053 86 l g 1054 85 l g 1055 84 l g 1057 83 l g 1058 82 l g 1059 81 l g g 1061 80 l g g 1063 79 l g g 1065 78 l g g g 1068 77 l g g 1071 76 l g g g g 1075 75 l g g g g g g g g g g g j g g g g i g g g i g g g i g g i g j g i g g i g i g i g j g i g i g i g i g i i g i g i g i i g i g i i g i i g i i g i i i g i i i g i i i i 1123 112 l 1123 111 l g 1124 110 l 1124 109 l 1124 108 l 1124 107 l g 1125 106 l 1125 105 l 1126 104 l 1126 103 l 1126 102 l g 1127 101 l 1127 100 l g 1128 99 l 1128 98 l g 1129 97 l 1130 96 l 1130 95 l g 1131 94 l g 1132 93 l 1132 92 l g 1133 91 l g 1134 90 l g 1135 89 l g 1136 88 l g 1137 87 l 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427 269 l i i 426 271 l i i 425 273 l i 424 275 l i 423 276 l i 422 277 l i 421 278 l i 420 279 l i 419 280 l 418 280 l i 417 281 l 416 281 l i 415 282 l 414 282 l 414 281 l 413 281 l 412 281 l 412 280 l 412 279 l 412 278 l 412 277 l 412 276 l g 413 275 l 413 274 l g 414 273 l 415 272 l 415 271 l g 416 270 l g 417 269 l g 418 268 l g 420 267 l g 421 266 l g 423 265 l g 424 264 l g g g 427 263 l g g 430 262 l g g g g 434 261 l g g g g g g g g i g g g g i g g j g i g g i g i g i g i g i g i i g i i g i i g i i i i i g i i i i i i i 460 288 l i i i i i 459 293 l i i i 458 296 l i i 457 298 l s 457 298 m i i 456 300 l i i 455 302 l i 454 303 l i 453 304 l i 452 305 l i 451 306 l i 450 307 l i 449 308 l 448 309 l 447 309 l 446 309 l 445 309 l 444 309 l 443 309 l 443 308 l 443 307 l 442 307 l 442 306 l g 443 305 l 443 304 l 443 303 l g 444 302 l 444 301 l g 445 300 l g 446 299 l 447 298 l 448 297 l 449 296 l g 450 295 l g 451 294 l g g 453 293 l g 455 292 l g 457 291 l g g 459 290 l g g g g 463 289 l g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i i g i j i j i i i g i i i i i i i i i i i i i 490 319 l i i i 489 323 l i i 488 325 l i i 487 327 l i i 486 329 l i 485 330 l i i 484 332 l i 483 333 l i 482 334 l i 481 335 l 480 336 l 479 336 l i 478 337 l 477 337 l 476 337 l 475 337 l 474 337 l 474 336 l 473 336 l 473 335 l 473 334 l 473 333 l 473 332 l g 474 331 l 474 330 l g 475 329 l 475 328 l g 476 327 l g 477 326 l g 478 325 l g 479 324 l g 480 323 l g 482 322 l g 483 321 l g g 485 320 l g g 487 319 l g g 489 318 l g g g g 493 317 l g g g g g g g g g g g g i g g g i g g i g g i g i g g i g i j i g i g i i g i i j i i i i g i i i i i i i i i 521 345 l i i i i 520 349 l i i i 519 352 l i i 518 354 l i i 517 356 l i 516 358 l i 515 359 l i 514 360 l i 513 361 l i 512 362 l i 511 363 l i 510 364 l 509 364 l i 508 365 l 507 365 l 506 365 l 505 365 l 505 364 l 504 364 l 504 363 l 504 362 l 504 361 l 504 360 l 504 359 l g 505 358 l 505 357 l g 506 356 l 506 355 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464 l i i 640 466 l i i 639 468 l i 638 469 l i 637 470 l i i 636 472 l i 635 473 l 634 474 l 633 474 l i 632 475 l i 631 476 l 630 476 l 629 476 l 628 476 l 627 476 l 627 475 l 626 475 l 626 474 l 626 473 l 626 472 l 626 471 l 626 470 l g 627 469 l 627 468 l g 628 467 l g 629 466 l g 630 465 l g 631 464 l g 632 463 l g 633 462 l g 634 461 l g g 636 460 l g g 638 459 l g g 640 458 l g g 642 457 l g g g g 646 456 l g g g g g g g g g g g g i g g g i g g i g g i g i g i g i g i g i g i j i i g i i g i i i i i g i i i i i i 674 483 l i i i i 673 488 l i i 672 490 l i i i 671 493 l i i 670 495 l i 669 496 l i i 668 498 l i 667 499 l i 666 500 l i 665 501 l i 664 502 l 663 503 l 662 503 l i 661 504 l 660 504 l 659 504 l 658 504 l 657 504 l 657 503 l 657 502 l 656 502 l 656 501 l 656 500 l g 657 499 l 657 498 l 657 497 l g 658 496 l 659 495 l 659 494 l g 660 493 l g 661 492 l g 662 491 l g 663 490 l g 665 489 l g 666 488 l g g 668 487 l g g 670 486 l g g 672 485 l g g g 676 484 l g g g g g g g g g g g g g i g g g i g g i g g i g i g i g i g i g i j i g i i g i i i i g i i i i i i i i i i i i 704 514 l i i i 703 517 l i i 702 520 l i i 701 522 l i 700 524 l i 699 525 l i 698 526 l i 697 527 l i 696 528 l i 695 529 l i 694 530 l i 693 531 l 692 531 l i 691 532 l 690 532 l 689 532 l 688 532 l 688 531 l 687 531 l 687 530 l 687 529 l 687 528 l 687 527 l 687 526 l g 688 525 l 688 524 l g 689 523 l g 690 522 l 691 521 l 692 520 l 693 519 l g 694 518 l g 695 517 l g 696 516 l g g 698 515 l g g 700 514 l g g 702 513 l g g g 705 512 l g g g g g g 712 511 l g g j g g g g g i g g g i g g i g j g i g i g i g i j i g i i g i i g i i i i j i i i i i i i i 735 539 l i i i i i 734 544 l i i 733 547 l i i 732 549 l i 731 551 l i 730 552 l i 729 553 l i i 728 555 l i 727 556 l i 726 557 l 725 558 l 724 558 l i 723 559 l 722 559 l i 721 560 l 720 560 l 719 560 l 719 559 l 718 559 l 718 558 l 718 557 l 718 556 l 718 555 l 718 554 l 718 553 l g 719 552 l 719 551 l g 720 550 l g 721 549 l g 722 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l g 1047 405 l g 1048 404 l g g 1050 403 l g g 1052 402 l g g 1054 401 l g g g g 1058 400 l g g g g g g g g i g g g g j g g i g g j g i g g i g j g i g i g i g i j i g i i g i i i i i 1087 420 l 1086 420 l i 1085 421 l 1084 421 l 1084 420 l 1083 420 l 1082 420 l 1081 419 l 1080 419 l 1080 418 l 1079 418 l 1079 417 l 1078 417 l 1078 416 l 1077 416 l 1077 415 l 1076 415 l 1076 414 l 1075 414 l 1075 413 l 1075 412 l 1074 412 l 1074 411 l 1074 410 l 1073 410 l 1073 409 l 1073 408 l 1072 408 l 1072 407 l 1072 406 l 1071 406 l 1071 405 l 1071 404 l 1071 403 l 1071 402 l 1070 402 l 1070 401 l 1070 400 l 1070 399 l 1070 398 l 1070 397 l 1070 396 l 1070 395 l 1070 394 l 1070 393 l 1070 392 l 1070 391 l 1070 390 l 1071 389 l 1071 388 l 1071 387 l 1071 386 l g 1072 385 l 1072 384 l g 1073 383 l 1073 382 l g 1074 381 l g 1075 380 l g 1076 379 l g 1077 378 l g 1078 377 l g 1079 376 l g 1081 375 l g 1083 374 l g g 1085 373 l g g g g g 1091 372 l g g g g i g g g g g j g g i g g g i g g i g i g g i g i g i g i g i g i g i i g i i i g i i 1118 391 l i 1117 392 l i 1116 393 l 1115 393 l 1114 393 l 1114 392 l 1113 392 l 1112 392 l 1112 391 l 1111 391 l 1110 391 l 1110 390 l 1109 390 l 1109 389 l 1108 389 l 1108 388 l 1107 388 l 1107 387 l 1106 386 l 1106 385 l 1105 385 l 1105 384 l 1104 383 l 1104 382 l 1103 381 l 1103 380 l 1103 379 l 1102 379 l 1102 378 l 1102 377 l 1102 376 l 1101 376 l 1101 375 l 1101 374 l 1101 373 l 1101 372 l 1101 371 l 1100 371 l 1100 370 l 1100 369 l 1100 368 l 1100 367 l 1100 366 l 1100 365 l g 1101 364 l 1101 363 l 1101 362 l 1101 361 l 1101 360 l g 1102 359 l 1102 358 l 1102 357 l g 1103 356 l 1103 355 l g 1104 354 l g 1105 353 l 1106 352 l 1107 351 l 1107 350 l g 1109 349 l g 1110 348 l g 1112 347 l g 1114 346 l g g 1117 345 l g g g g g g g g g g g g g i g g g j g g i g g i g j g i g i g j j j i g i g i i g i i i i i 1148 364 l i 1147 365 l 1146 365 l 1145 365 l 1144 365 l 1144 364 l 1143 364 l 1142 364 l 1142 363 l 1141 363 l 1141 362 l 1140 362 l 1140 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y Fq(2)2092 4901 y Fm(>)g(U)2270 4916 y Fq(3)2346 4901 y Fm(>)f(U)2523 4916 y Fq(1)2563 4901 y Fu(.)44 b(In)30 b(other)f(w)o(ords,)h(Fig.)f(3)g(contra-)0 5022 y(dicts)h(a)g(\223Kirchof)n(f)5 b(')-5 b(s)31 b(La)o(w\224)f(on)g (current)h(loops.)46 b(Such)31 b(an)f(e)o(xample)g(can)h(also)f(be)g (constructed)g(when)g(the)0 5142 y(\223triangle\224)25 b(is)f(in)g(the)h(center)g(of)g(a)g(chain)g(connecting)f(tw)o(o)h(heat) f(baths.)p Black 0 5388 a Fo(Example)h(3)p Black 49 w Fu(Three)g(connected)g(heat)g(baths)f(with)g(dif)n(ferent)g(coupling)g (constants)p Black Black eop %%Page: 6 6 6 5 bop Black 0 266 a Fo(6)3189 b Fu(H)t Fh(E)t(A)-5 b(T)31 b(FL)t(U)t(X)t(E)t(S)p Black Black Black Black 1359 1521 a @beginspecial 0 @llx 0 @lly 133 @urx 126 @ury 1329 @rwi @setspecial %%BeginDocument: example3.eps %!PS-Adobe-2.0 %%BoundingBox: 0 0 133 126 %%Title: example3.eps %%Creator: Martin's amazing postscript figure generator %%Pages: 1 %%PageOrder: Ascend %%EndComments /m {moveto} def /rm {rmoveto} def /l {lineto} def /rl {rlineto} def /n {newpath} def /cl {closepath} def /s {stroke} def /srgb {setrgbcolor} def /lw {setlinewidth} def /f {fill} def /it {/Times-Italic findfont} def /ro {/Times-Roman findfont} def /bf {/Times-Bold findfont} def /bi {/Times-BoldItalic findfont} def /sy {/Symbol findfont} def /sc {scalefont} def /sw {stringwidth} def /sf {setfont} def /cp {currentpoint} def /gs {gsave} def /gr {grestore} def /sd {setdash} def /t {show} def /b {-1 -1 rl} def /c {0 -1 rl} def /d {1 -1 rl} def /e {-1 0 rl} def /g {1 0 rl} def /h {-1 1 rl} def /i {0 1 rl} def /j {1 1 rl} def 1 setlinejoin /adict 5 dict def /ato { adict begin /len exch def /py exch def /px exch def cp /opy exch def /opx exch def px py l gs [] 0 sd 0 setlinejoin px py translate px opx ne py opy ne or { py opy sub px opx sub atan rotate n 0 0 m len neg len 3 div rl len 5 div len 3 div neg rl len 5 div neg len 3 div neg rl cl gs f gr s } {0 0 m 0 0 l} ifelse gr end } def /ellipsedict 8 dict def ellipsedict 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220 l 790 220 l 789 220 l 789 219 l 788 219 l 788 218 l 787 218 l 787 217 l 787 216 l 786 216 l 786 215 l 786 214 l 786 213 l 786 212 l 786 211 l 786 210 l 786 209 l 786 208 l 786 207 l 786 206 l 786 205 l 786 204 l 786 203 l g 787 202 l 787 201 l 787 200 l g 788 199 l 788 198 l g 789 197 l 789 196 l g 790 195 l 791 194 l 791 193 l g 792 192 l g 793 191 l g 794 190 l g 795 189 l g 796 188 l g 797 187 l g 799 186 l s 799 186 m g 800 185 l g g 802 184 l g g g 805 183 l g g g g 809 182 l g g g g g g g i g g g g i g g g i g g i g j g i g i g i g i g i g i g i g i i g i i g i i g i i i g i i i i i i g i i 839 211 l i i i i i 838 216 l i i 837 218 l i 836 219 l i 835 220 l 834 220 l 833 220 l 832 220 l 832 219 l 831 219 l 831 218 l 830 218 l 830 217 l 829 217 l 829 216 l 829 215 l 829 214 l 828 214 l 828 213 l 828 212 l 828 211 l 828 210 l 828 209 l 828 208 l 828 207 l 828 206 l 828 205 l g 829 204 l 829 203 l 829 202 l 829 201 l g 830 200 l 830 199 l g 831 198 l 831 197 l g 832 196 l 832 195 l g 833 194 l g 834 193 l 834 192 l g 835 191 l g 836 190 l g 837 189 l g 838 188 l g 840 187 l g 841 186 l g g 843 185 l g g 845 184 l g g 847 183 l g g g g 852 182 l g g g g g g j g g g g i g g i g g i g g i g i g g i g i g i g i j i g i g i i g i i g i i j i i i g i i i i i i i i i 881 214 l i i i 880 217 l i 879 218 l i 878 219 l i 877 220 l 876 220 l 875 220 l 874 220 l 874 219 l 873 219 l 873 218 l 872 218 l 872 217 l 872 216 l 871 216 l 871 215 l 871 214 l 871 213 l 871 212 l 870 212 l 870 211 l 870 210 l 870 209 l 870 208 l g 871 207 l 871 206 l 871 205 l 871 204 l 871 203 l g 872 202 l 872 201 l 872 200 l g 873 199 l 873 198 l 874 197 l 874 196 l g 875 195 l 875 194 l g 876 193 l g 877 192 l g 878 191 l g 879 190 l g 880 189 l g 881 188 l g 882 187 l g 883 186 l g g 885 185 l g g 887 184 l g g g 890 183 l g g g g 894 182 l g g g g g g g i g g g g i g g g i g g i g i g g i g i g i g i g i g i g i i g i g i i g i i g i i i g i i i i i i i i i i i i 923 215 l i i 922 218 l i 921 219 l i 920 220 l 919 220 l 918 220 l 917 220 l 917 219 l 916 219 l 915 218 l 915 217 l 914 217 l 914 216 l 914 215 l 913 215 l 913 214 l 913 213 l 913 212 l 913 211 l 913 210 l 913 209 l 913 208 l 913 207 l 913 206 l 913 205 l 913 204 l g 914 203 l 914 202 l 914 201 l g 915 200 l 915 199 l 916 198 l 916 197 l g 917 196 l 917 195 l g 918 194 l 919 193 l 919 192 l g 920 191 l g 921 190 l g 922 189 l g 923 188 l g 924 187 l g g 926 186 l g 928 185 l g 930 184 l g g 932 183 l g g g g 936 182 l g g g g g g g i g g g g j g g i g g i g g i g i g j g i j j i g i g i j i g i i g i i s n 252 242 m 251 242 l i 250 243 l i 249 244 l i 248 245 l i i 247 247 l i 246 248 l i 245 250 l i 244 252 l i i 243 254 l i i i 242 258 l i i i i i i i g i i i j i i g i g i j i g i g j g i g i g g i g g i g g g i g g g g g i g g g g g g g g g g g 275 282 l g g g g g 280 281 l g g g 283 280 l g g 285 279 l g g 287 278 l g 288 277 l g g 290 276 l g 291 275 l g 292 274 l 292 273 l 292 272 l g 293 271 l 292 271 l 292 270 l 291 270 l 291 269 l 290 269 l 289 269 l 288 269 l 287 269 l 286 269 l 285 269 l 284 269 l 283 269 l 282 269 l i 281 270 l 280 270 l i 279 271 l 278 271 l i 277 272 l 276 272 l i 275 273 l i 274 274 l 273 274 l i 272 275 l i 271 276 l i 270 277 l i 269 278 l i 268 279 l i 267 281 l i 266 282 l i i 265 284 l i 264 286 l i i 263 288 l i i i 262 292 l i i i i i i i g i i i j i j i g i g i i g i g g i g i g j g i g g j g g j g g g g i g g g g g g g g g g 295 316 l g g g g 300 315 l g g 303 314 l g g 305 313 l g g 307 312 l g 308 311 l g g 310 310 l g 311 309 l 312 308 l 312 307 l 312 306 l g 313 305 l 312 305 l 312 304 l 311 304 l 311 303 l 310 303 l 309 303 l 308 303 l 308 302 l 307 302 l i 306 303 l 305 303 l 304 303 l 303 303 l 302 303 l i 301 304 l 300 304 l i 299 305 l 298 305 l i 297 306 l 296 306 l i 295 307 l 294 308 l 293 308 l i 292 309 l i 291 310 l i 290 311 l i 289 312 l i 288 313 l i 287 314 l i i 286 316 l i 285 318 l i 284 319 l i i i 283 322 l i i i i 282 326 l i i i i i i i g i i i g i i g i i g i g i j j g i g i g g i g i g g g i g g g i g g g g g i g g g g g g g g g 314 350 l g g g g g 319 349 l g g g 322 348 l g g g 325 347 l g g 327 346 l g 328 345 l g g 330 344 l g 331 343 l 331 342 l g 332 341 l 333 340 l 333 339 l 332 339 l 332 338 l 332 337 l 331 337 l 330 337 l 329 337 l 329 336 l 328 336 l 327 336 l 326 336 l i 325 337 l 324 337 l 323 337 l 322 337 l i 321 338 l 320 338 l 319 339 l 318 339 l i 317 340 l 316 340 l i 315 341 l 314 342 l 313 342 l i 312 343 l i 311 344 l i 310 345 l i 309 346 l i 308 347 l i 307 349 l i 306 350 l i 305 352 l i 304 354 l i i 303 356 l i i i i 302 360 l i i i i i i g i i i i g i i g i i g i g i g i g i g i g i g g i g j g g i g g g i g g g g g j g g g g g g g 333 384 l g g g g g g 339 383 l g g g 342 382 l g g g 345 381 l g 347 380 l g 348 379 l g 350 378 l g 351 377 l 352 376 l 352 375 l 353 374 l 353 373 l 352 373 l 352 372 l 352 371 l 351 371 l 350 371 l 349 370 l 348 370 l 347 370 l 346 370 l i 345 371 l 344 371 l 343 371 l 342 371 l i 341 372 l 340 372 l 339 372 l i 338 373 l 337 374 l 336 374 l i 335 375 l 334 376 l 333 376 l i 332 377 l i 331 378 l i 330 379 l i 329 380 l i 328 381 l i 327 382 l i i 326 384 l i 325 386 l i 324 387 l i i i 323 390 l i i i i 322 394 l i i i i i i g i i i i g i i g i i g i g i g i g i g i g i g g i g g i g g i g g g i g g g g g g j g g g g g 352 418 l g g g g g g g 359 417 l g g g 362 416 l g g 365 415 l g 367 414 l g 368 413 l g 370 412 l g 371 411 l 371 410 l s 371 410 m g 372 409 l 373 408 l 373 407 l 372 406 l 372 405 l 371 405 l 370 405 l 370 404 l 369 404 l 368 404 l 367 404 l 366 404 l 365 404 l i 364 405 l 363 405 l 362 405 l i 361 406 l 360 406 l 359 406 l i 358 407 l 357 408 l 356 408 l i 355 409 l 354 409 l i 353 410 l i 352 411 l i 351 412 l i 350 413 l i 349 414 l i 348 415 l i 347 417 l i 346 418 l i 345 419 l i i 344 421 l i i i 343 424 l i i i i 342 428 l i i i i i i g i i i i g i i g i j i g i g i g i g i g i g g i g g i g g j g g g i g g g g g g g i g g g 371 452 l g g g g g g g 379 451 l g g g 382 450 l g g 384 449 l g g 386 448 l g g 388 447 l g 389 446 l g 391 445 l 391 444 l g 392 443 l g 393 442 l 393 441 l 393 440 l 392 440 l 392 439 l 391 439 l 390 439 l 390 438 l 389 438 l 388 438 l 387 438 l 386 438 l 385 438 l i 384 439 l 383 439 l 382 439 l 381 440 l 380 440 l 379 440 l i 378 441 l 377 441 l i 376 442 l i 375 443 l 374 443 l i 373 444 l i 372 445 l i 371 446 l i 370 447 l i 369 448 l i 368 449 l i 367 450 l i i 366 452 l i 365 454 l i 364 456 l i i 363 458 l i i i i 362 462 l i i i i i i g i i i j i i g i j i g i g i g i g i g j g i g g i g g g i g g g i g g g g g g g g g g g g g g g g g 398 485 l g g g g 402 484 l g g 404 483 l g g 406 482 l g g 408 481 l g 409 480 l g 411 479 l 411 478 l g 412 477 l g 413 476 l 413 475 l 413 474 l 412 474 l 412 473 l 411 473 l 410 473 l 410 472 l 409 472 l 408 472 l 407 472 l 406 472 l 405 472 l 404 473 l 403 473 l 402 473 l 401 473 l i 400 474 l 399 474 l i 398 475 l 397 475 l i 396 476 l i 395 477 l 394 477 l i 393 478 l i 392 479 l i 391 480 l i 390 481 l i 389 482 l i 388 483 l i 387 484 l i i 386 486 l i 385 487 l i i 384 489 l i i i 383 492 l i i i i 382 497 l i i i i g i i i i g i i i g i g i i g i g i g i g i g g i g i g g j g g i g g g i g g g g g g g g g g g g g g g g g 418 519 l g g g 422 518 l g g 424 517 l g g 426 516 l g g 428 515 l g 429 514 l g 430 513 l g 431 512 l g 432 511 l 433 510 l 433 509 l 433 508 l 432 508 l 432 507 l 431 507 l 431 506 l 430 506 l 429 506 l 428 506 l 427 506 l 426 506 l 425 506 l 424 506 l i 423 507 l 422 507 l 421 507 l i 420 508 l 419 508 l i 418 509 l 417 509 l i 416 510 l 415 511 l 414 511 l i 413 512 l i 412 513 l i 411 514 l i 410 515 l i 409 516 l i 408 517 l i 407 518 l i i 406 520 l i 405 521 l i i 404 524 l i i 403 526 l i i i i 402 531 l i i i i g i i i i g i i j i g i i g i g i g i g i g g i g j g g i g g i g g g g i g g g g g g g g g g g g g g g 438 553 l g g g 441 552 l g g g 444 551 l g g 446 550 l g g 448 549 l g 449 548 l g 450 547 l g 451 546 l g 452 545 l 453 544 l 453 543 l 453 542 l 452 542 l 452 541 l 451 541 l 451 540 l 450 540 l 449 540 l 448 540 l 447 540 l 446 540 l 445 540 l 444 540 l i 443 541 l 442 541 l 441 541 l i 440 542 l 439 542 l i 438 543 l s 438 543 m 437 543 l i 436 544 l 435 545 l 434 545 l i 433 546 l i 432 547 l i 431 548 l i 430 549 l i 429 550 l i 428 551 l i 427 552 l i i 426 554 l i 425 555 l i i 424 557 l i i i 423 560 l i i i i i 422 565 l i i i j i i i i g i i j i g i i g i g i g i g j g i g g i g g i g g i g g g g i g g g g g g g g g g g g g g g 457 587 l g g g g 461 586 l g g g 464 585 l g g 466 584 l g g 468 583 l g 469 582 l g 470 581 l g 471 580 l g 472 579 l g 473 578 l 473 577 l 473 576 l 472 576 l 472 575 l 471 575 l 471 574 l 470 574 l 469 574 l 468 574 l 467 574 l 466 574 l 465 574 l 464 574 l i 463 575 l 462 575 l 461 575 l i 460 576 l 459 576 l i 458 577 l 457 577 l i 456 578 l 455 578 l i 454 579 l i 453 580 l i 452 581 l i 451 582 l i 450 583 l i 449 584 l i 448 585 l i 447 586 l i i 446 588 l i 445 590 l i 444 592 l i i 443 594 l i i i i i 442 599 l i i i g i i i i i g i i g i i g i j j i g j g i g i g g i g g i g g j g g g g i g g g g g g g g g g g g g g 477 621 l g g g g 481 620 l g g g 484 619 l g g 486 618 l g g 488 617 l g 489 616 l g 490 615 l g 491 614 l g 492 613 l g 493 612 l 493 611 l 493 610 l 492 610 l 492 609 l 491 609 l 491 608 l 490 608 l 489 608 l 488 608 l 487 608 l 486 608 l 485 608 l 484 608 l 483 609 l 482 609 l 481 609 l i 480 610 l 479 610 l i 478 611 l 477 611 l i 476 612 l 475 612 l i 474 613 l i 473 614 l i 472 615 l i 471 616 l i 470 617 l i 469 618 l i 468 619 l i 467 620 l i i 466 622 l i 465 623 l i i 464 625 l i i i 463 628 l i i i i i 462 634 l i i g i i i i i g i i g i i g i g i j j j g i g i g g i g g i g g g i g g g g i g g g g g g g g g g g g g 497 655 l g g g g 501 654 l g g 504 653 l g g 506 652 l g 508 651 l g 509 650 l g 510 649 l g 511 648 l g 512 647 l g 513 646 l 513 645 l 513 644 l 512 644 l 512 643 l 511 643 l 511 642 l 510 642 l 509 642 l 508 642 l 507 642 l 506 642 l 505 642 l 504 642 l 503 642 l i 502 643 l 501 643 l i 500 644 l 499 644 l 498 645 l 497 645 l i 496 646 l 495 646 l i 494 647 l i 493 648 l i 492 649 l 491 650 l i 490 651 l i 489 652 l i 488 653 l i 487 654 l i i 486 656 l i 485 657 l i i 484 659 l i i i 483 662 l i i i i i i i i i i i i i g i i g i i g i g i g i g i g i g i g j g i g g i g g g i g g g g i g g g g g g g g g g g g g 516 689 l g g g g 521 688 l g g 524 687 l g g 526 686 l g 528 685 l g 529 684 l g 530 683 l g 531 682 l g 532 681 l 533 680 l 533 679 l 533 678 l 533 677 l 532 677 l 532 676 l 531 676 l 530 676 l 529 676 l 528 676 l 527 676 l 526 676 l 525 676 l 524 676 l 523 676 l i 522 677 l 521 677 l 520 678 l 519 678 l 518 678 l i 517 679 l i 516 680 l 515 680 l i 514 681 l i 513 682 l i 512 683 l 511 684 l 510 685 l 509 686 l i 508 687 l i 507 688 l i 506 690 l i 505 691 l i i 504 693 l i i i 503 696 l i i i i i i i i i i i i j i i g i i g i g i g i g i g i g i g j g i g g j g g j g g g g i g g g g g g g g g g g 536 723 l g g g g 540 722 l g g g 543 721 l g g 546 720 l g 547 719 l g g 549 718 l g 550 717 l s 550 717 m g 551 716 l g 552 715 l 553 714 l 553 713 l 553 712 l 553 711 l 552 711 l 552 710 l 551 710 l 550 710 l 549 710 l 548 710 l 547 710 l 546 710 l 545 710 l 544 710 l 543 710 l i 542 711 l 541 711 l 540 711 l i 539 712 l 538 712 l i 537 713 l i 536 714 l 535 714 l i 534 715 l i 533 716 l i 532 717 l 531 717 l i 530 718 l i 529 720 l i 528 721 l i 527 722 l i 526 724 l i 525 725 l i i 524 727 l i i i 523 730 l i i i i i i i i i i i i g i i i g i i g i g i g i g i g i g i g g i g j g g i g g g i g g g g j g g g g g g g g g g 555 757 l g g g g g 560 756 l g g g 563 755 l g g 565 754 l g g 567 753 l g g 569 752 l g 570 751 l g 571 750 l g 572 749 l g 573 748 l 573 747 l 573 746 l 573 745 l 572 745 l 572 744 l 571 744 l 570 744 l 569 744 l 568 744 l 567 744 l 566 744 l 565 744 l 564 744 l 563 744 l i 562 745 l 561 745 l 560 745 l i 559 746 l 558 746 l i 557 747 l 556 748 l 555 748 l i 554 749 l i 553 750 l 552 751 l 551 752 l 550 753 l 549 754 l i 548 755 l i 547 756 l i 546 758 l i 545 759 l i i 544 761 l i i i 543 764 l i i i i i i i i i i i i g i i i g i j i g i g i g i g i g i g g i g g i g g i g g g i g g g g g i g g g g g g g g g 575 791 l g s n 992 242 m i g i j i g i i g i i g i i g i i i g i i i i i i g i i i 999 264 l i i i i i 998 270 l i i 997 272 l i i 996 274 l i i 995 276 l i 994 277 l i i 993 279 l i 992 280 l i 991 281 l i 990 282 l 989 283 l 988 283 l i 987 284 l i 986 285 l 985 285 l i 984 286 l 983 286 l i 982 287 l 981 287 l i 980 288 l 979 288 l 978 288 l i 977 289 l 976 289 l 975 289 l 974 289 l i 973 290 l 972 290 l 971 290 l 970 290 l 969 290 l 968 290 l 967 290 l i 966 291 l 965 291 l 964 291 l 963 291 l 963 290 l 962 290 l 961 290 l 960 290 l 959 290 l 958 290 l 957 290 l 956 290 l 955 290 l 955 289 l 954 289 l 953 289 l 952 289 l 951 288 l 950 288 l 949 288 l 949 287 l 948 287 l 947 287 l 947 286 l 946 286 l 946 285 l 945 285 l 944 284 l 944 283 l 944 282 l g g g g g i g g j g i g g i g i g i g g i g i g i g i i g i g i g i i g i i g i i g i i j i i i j i i i i i i i i i 969 317 l i i i i 968 321 l i i 967 323 l i i 966 325 l i i 965 327 l i 964 328 l i 963 329 l i 962 330 l i 961 331 l i 960 332 l i 959 333 l i 958 334 l 957 334 l i 956 335 l i 955 336 l 954 336 l i 953 337 l 952 337 l 951 338 l 950 338 l 949 338 l i 948 339 l 947 339 l 946 339 l 945 339 l i 944 340 l 943 340 l 942 340 l 941 340 l 940 340 l 939 340 l 938 341 l 937 341 l 936 341 l 935 341 l 934 341 l 933 341 l 932 341 l 932 340 l 931 340 l 930 340 l 929 340 l 928 340 l 927 340 l 926 340 l 925 340 l 925 339 l 924 339 l 923 339 l 922 339 l 922 338 l 921 338 l 920 338 l 919 338 l 919 337 l 918 337 l 917 337 l 917 336 l 916 336 l 916 335 l 915 335 l 915 334 l 914 334 l 914 333 l 914 332 l g g g g g i g g g i g g i g i g j g i g i g i g i g i g i j i g i g i i g i i g i i j i i i g i i i i i i i i i i i i i 939 369 l i i i 938 372 l i i 937 374 l i i 936 376 l i 935 378 l i 934 379 l i 933 380 l i 932 381 l i 931 382 l i 930 383 l 929 383 l i 928 384 l i 927 385 l 926 385 l i 925 386 l 924 386 l i 923 387 l 922 387 l i 921 388 l 920 388 l 919 389 l 918 389 l 917 389 l 916 389 l i 915 390 l 914 390 l 913 390 l 912 390 l 911 390 l 910 390 l i 909 391 l 908 391 l 907 391 l 906 391 l 905 391 l 904 391 l 903 391 l 902 391 l 901 391 l 901 390 l 900 390 l 899 390 l 898 390 l 897 390 l 896 390 l 895 390 l 895 389 l 894 389 l 893 389 l 892 389 l 892 388 l 891 388 l 890 388 l 889 387 l 888 387 l 888 386 l 887 386 l 886 386 l 886 385 l 885 385 l 885 384 l 885 383 l 885 382 l g g g g i g g g i g g i g i g g i g i g i g i g i g i g i g i g i i g i g i i g i i g i i i g i i i i j i i i i i i i i 910 417 l i i i i 909 421 l i i 908 423 l i i 907 425 l i i 906 427 l i 905 428 l i 904 429 l i 903 430 l i 902 431 l i 901 432 l s 901 432 m i 900 433 l i 899 434 l 898 434 l i 897 435 l i 896 436 l 895 436 l i 894 437 l 893 437 l i 892 438 l 891 438 l 890 438 l i 889 439 l 888 439 l 887 439 l i 886 440 l 885 440 l 884 440 l 883 440 l 882 440 l 881 440 l i 880 441 l 879 441 l 878 441 l 877 441 l 876 441 l 875 441 l 874 441 l 873 441 l 872 441 l 871 441 l 871 440 l 870 440 l 869 440 l 868 440 l 867 440 l 866 440 l 865 440 l 865 439 l 864 439 l 863 439 l 862 439 l 862 438 l 861 438 l 860 438 l 860 437 l 859 437 l 858 437 l 858 436 l 857 436 l 857 435 l 856 435 l 856 434 l 855 434 l 855 433 l 855 432 l g g g g g i g g i g g i g g i g i g j g i g i g i g i j i g i g i i g i j i j i i g i i i g i i i i i i i i i i i i i 880 469 l i i i 879 472 l i i 878 474 l i i 877 476 l i 876 477 l i i 875 479 l i 874 480 l i 873 481 l i 872 482 l i 871 483 l 870 484 l 869 484 l i 868 485 l 867 485 l i 866 486 l 865 487 l 864 487 l 863 488 l 862 488 l 861 488 l i 860 489 l 859 489 l 858 489 l 857 490 l 856 490 l 855 490 l 854 490 l 853 490 l 852 490 l i 851 491 l 850 491 l 849 491 l 848 491 l 847 491 l 846 491 l 845 491 l 844 491 l 843 491 l 842 491 l 841 491 l 841 490 l 840 490 l 839 490 l 838 490 l 837 490 l 836 490 l 835 489 l 834 489 l 833 489 l 832 489 l 832 488 l 831 488 l 830 488 l 830 487 l 829 487 l 828 487 l 828 486 l 827 486 l 827 485 l 826 485 l 826 484 l 825 483 l g 826 482 l g g g g i g g j g i g g i g j g i g i g i g i g i g i g i i g i g i i g i i g i i g i i i g i i i i i g i i i i i i 851 516 l i i i i 850 521 l i i 849 523 l i i 848 525 l i i 847 527 l i 846 528 l i 845 529 l i 844 530 l i 843 531 l i 842 532 l i 841 533 l i 840 534 l 839 535 l 838 535 l i 837 536 l 836 536 l i 835 537 l 834 537 l i 833 538 l 832 538 l 831 539 l 830 539 l 829 539 l 828 539 l i 827 540 l 826 540 l 825 540 l 824 540 l 823 540 l i 822 541 l 821 541 l 820 541 l 819 541 l 818 541 l 817 541 l 816 541 l 815 541 l 814 541 l 813 541 l 812 541 l 811 541 l 811 540 l 810 540 l 809 540 l 808 540 l 807 540 l 806 540 l 806 539 l 805 539 l 804 539 l 803 539 l 803 538 l 802 538 l 801 538 l 800 538 l 800 537 l 799 537 l 799 536 l 798 536 l 797 536 l 797 535 l 796 535 l 796 534 l 796 533 l 797 532 l g g g i g g g i g g i g i g g i g i g i g i g i g i g i g i g i j i g i i g i i g i i j i i i g i i i i i i i i i i i 821 568 l i i i i 820 572 l i i 819 574 l i i 818 576 l i 817 577 l i i 816 579 l i 815 580 l i 814 581 l i 813 582 l i 812 583 l i 811 584 l 810 584 l i 809 585 l 808 586 l 807 586 l i 806 587 l 805 587 l i 804 588 l s 804 588 m 803 588 l 802 588 l i 801 589 l 800 589 l 799 589 l i 798 590 l 797 590 l 796 590 l 795 590 l 794 590 l i 793 591 l 792 591 l 791 591 l 790 591 l 789 591 l 788 591 l 787 591 l 786 591 l 785 591 l 784 591 l 783 591 l 782 591 l 781 591 l 780 591 l 780 590 l 779 590 l 778 590 l 777 590 l 776 590 l 776 589 l 775 589 l 774 589 l 773 589 l 773 588 l 772 588 l 771 588 l 771 587 l 770 587 l 769 587 l 769 586 l 768 586 l 768 585 l 767 585 l 767 584 l 766 584 l 766 583 l g 767 582 l g g g i g g g i g g i g g i g i g j g i g i g i g i g i i g i g i j i g i i g i i j i i j i i i i i g i i i i 792 615 l i i i i i 791 620 l i i i 790 623 l i i 789 625 l i i 788 627 l i 787 628 l i 786 629 l i 785 630 l i 784 631 l i 783 632 l i 782 633 l i 781 634 l i 780 635 l 779 635 l i 778 636 l 777 637 l 776 637 l 775 637 l i 774 638 l 773 638 l i 772 639 l 771 639 l 770 639 l i 769 640 l 768 640 l 767 640 l 766 640 l 765 640 l i 764 641 l 763 641 l 762 641 l 761 641 l 760 641 l 759 641 l 758 641 l 757 641 l 756 641 l 755 641 l 754 641 l 753 641 l 752 641 l 751 641 l 750 641 l 750 640 l 749 640 l 748 640 l 747 640 l 746 640 l 746 639 l 745 639 l 744 639 l 743 639 l 743 638 l 742 638 l 741 638 l 741 637 l 740 637 l 739 637 l 739 636 l 738 636 l 738 635 l 737 635 l 737 634 l 737 633 l g 738 632 l g g i g g g i g g i g g i g j g i g i g i g i g i g i g i j i g i j i g i i g i i i g i i i i g i i i i i i i i i i 762 668 l i i i i 761 672 l i i 760 674 l i i 759 676 l i 758 677 l i i 757 679 l i 756 680 l i 755 681 l i 754 682 l i 753 683 l i 752 684 l 751 684 l i 750 685 l i 749 686 l 748 686 l i 747 687 l 746 687 l i 745 688 l 744 688 l 743 689 l 742 689 l 741 689 l 740 689 l i 739 690 l 738 690 l 737 690 l 736 690 l i 735 691 l 734 691 l 733 691 l 732 691 l 731 691 l 730 691 l 729 691 l 728 691 l 727 691 l 726 691 l 725 691 l 724 691 l 723 691 l 722 691 l 721 691 l 720 691 l 720 690 l 719 690 l 718 690 l 717 690 l 716 690 l 716 689 l 715 689 l 714 689 l 713 689 l 713 688 l 712 688 l 711 688 l 711 687 l 710 687 l 709 686 l 708 686 l 708 685 l 707 685 l 707 684 l 707 683 l g g 709 682 l g i g g g i g g g i g i g g i g i g i g i g j j i g i g i g i i g i i g i i g i i g i i i g i i i i i i i i i i i i i i 732 720 l i i i 731 723 l i i 730 725 l i i 729 727 l i 728 728 l i 727 729 l i 726 731 l 725 732 l 724 732 l i 723 733 l i 722 734 l i 721 735 l 720 735 l i 719 736 l 718 737 l 717 737 l i 716 738 l 715 738 l 714 738 l i 713 739 l 712 739 l 711 739 l i 710 740 l 709 740 l 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l s n 225 201 52 47 0 360 el gs 0.94 0.94 0.94 srgb f gr s n 1018 201 52 47 0 360 el gs 0.94 0.94 0.94 srgb f gr s n 622 815 52 47 0 360 el gs 0.94 0.94 0.94 srgb f gr s n 225 201 m n 1018 201 m n 622 815 m n 622 933 m n 132 118 m n 1112 118 m 12 lw n 585 616 m 400 329 33.3333 ato s n 784 421 m 718 524 33.3333 ato s n 489 272 m 754 272 33.3333 ato s showpage %%EndDocument @endspecial 1583 1320 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1583 1320 a 1566 1343 a Fd(2)1600 1320 y currentpoint grestore moveto 1600 1320 a 2373 1320 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 2373 1320 a 2356 1342 a Fd(3)2390 1320 y currentpoint grestore moveto 2390 1320 a 1978 709 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1978 709 a 1961 731 a Fd(1)1995 709 y currentpoint grestore moveto 1995 709 a 1978 591 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1978 591 a 1 1 1 TeXcolorrgb 1 1 1 TeXcolorrgb 1832 599 294 100 v 1 1 1 TeXcolorrgb Black 1 1 1 TeXcolorrgb Black 1840 576 a Fm(T)1897 591 y Fq(1)1964 576 y Fk(=)d(2)2117 591 y currentpoint grestore moveto 2117 591 a 1490 1403 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1490 1403 a 1 1 1 TeXcolorrgb 1 1 1 TeXcolorrgb 1316 1494 294 100 v 1 1 1 TeXcolorrgb Black 1 1 1 TeXcolorrgb Black 1324 1471 a Fm(T)1381 1486 y Fq(2)1449 1471 y Fk(=)f(1)1601 1403 y currentpoint grestore moveto 1601 1403 a 2466 1403 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 2466 1403 a 1 1 1 TeXcolorrgb 1 1 1 TeXcolorrgb 2348 1494 294 100 v 1 1 1 TeXcolorrgb Black 1 1 1 TeXcolorrgb Black 2356 1471 a Fm(T)2413 1486 y Fq(3)2480 1471 y Fk(=)h(1)2632 1403 y currentpoint grestore moveto 2632 1403 a Black 843 1724 a Fu(Figure)d(4:)30 b(Circulation)24 b(in)h(a)g(\223fully)f(thermalized\224)h(triangle)p Black 705 1845 a Fd(\()p Fq(\000)771 1855 y Fc(i)817 1845 y Fq(=)20 b(1)p Fj(;)11 b(V)999 1854 y Fb(12)1084 1845 y Fq(=)20 b Fj(V)1200 1854 y Fb(23)1284 1845 y Fq(=)g Ff(\000)p Fq(45)p Fj(;)12 b(V)1557 1854 y Fb(13)1641 1845 y Fq(=)20 b Ff(\000)p Fq(30)p Fj(;)12 b(\036)1915 1854 y Fb(1)p Fa(!)p Fb(2)2060 1845 y Fq(=)20 b(0)p Fj(:)p Fq(57)p Fj(;)12 b(\036)2334 1854 y Fb(2)p Fa(!)p Fb(3)2479 1845 y Fq(=)19 b(0)p Fj(:)p Fq(35)p Fj(;)12 b(\036)2752 1854 y Fb(3)p Fa(!)p Fb(1)2898 1845 y Fq(=)19 b(0)p Fj(:)p Fq(03)p Fd(\))p Black 0 2236 a Fu(The)32 b(e)o(xample)e(in)i(Fig.)f(4)h (sho)n(ws)e(that)h(the)h(circulation)e(of)i(Example)f(2)g(can)h(also)g (be)f(produced)h(when)f(all)0 2357 y(three)25 b(masses)f(are)i(in)e (contact)h(with)f(a)h(bath,)f(e)n(v)o(en)g(if)h(tw)o(o)f(baths)h(ha)n (v)o(e)f(the)h(same)f(temperature.)p Black 0 2592 a Fo(Example)h(4)p Black 49 w Fu(A)g(\223heat)g(pump\224)p Black Black Black 971 3755 a @beginspecial 0 @llx 0 @lly 226 @urx 113 @ury 2259 @rwi @setspecial %%BeginDocument: example4.eps %!PS-Adobe-2.0 %%BoundingBox: 0 0 226 113 %%Title: example4.eps %%Creator: Martin's amazing postscript figure generator %%Pages: 1 %%PageOrder: Ascend %%EndComments /m {moveto} def /rm {rmoveto} def /l {lineto} def /rl {rlineto} def /n {newpath} def /cl {closepath} def /s {stroke} def /srgb {setrgbcolor} def /lw {setlinewidth} def /f {fill} def /it {/Times-Italic findfont} def /ro {/Times-Roman findfont} def /bf {/Times-Bold findfont} def /bi {/Times-BoldItalic findfont} def /sy {/Symbol findfont} def /sc {scalefont} def /sw {stringwidth} def /sf {setfont} def /cp {currentpoint} def /gs {gsave} def /gr {grestore} def /sd {setdash} def /t {show} def /b {-1 -1 rl} def /c {0 -1 rl} def /d {1 -1 rl} def /e {-1 0 rl} def /g {1 0 rl} def /h {-1 1 rl} def /i {0 1 rl} def /j {1 1 rl} def 1 setlinejoin /adict 5 dict def /ato { adict begin /len exch def /py exch def /px exch def cp /opy exch def /opx exch def px py l gs [] 0 sd 0 setlinejoin px py translate px opx ne py opy ne or { py opy sub px opx sub atan rotate n 0 0 m len neg len 3 div rl len 5 div len 3 div neg rl len 5 div neg len 3 div neg rl cl gs f gr s } {0 0 m 0 0 l} ifelse gr end } def /ellipsedict 8 dict def ellipsedict /mtrx matrix put /el { ellipsedict begin /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix end } def 0.12 0.12 scale 4 lw [] 0 sd n 236 118 m 118 118 l s n 236 826 m 118 826 l s n 1653 118 m 1771 118 l s n 1653 826 m 1771 826 l s n 236 118 47 47 0 360 el gs 0.94 0.94 0.94 srgb f gr s n 945 118 47 47 0 360 el gs 0.94 0.94 0.94 srgb f gr s n 1653 118 47 47 0 360 el gs 0.94 0.94 0.94 srgb f gr s n 236 826 47 47 0 360 el gs 0.94 0.94 0.94 srgb f gr s n 945 826 47 47 0 360 el gs 0.94 0.94 0.94 srgb f gr s n 1653 826 47 47 0 360 el gs 0.94 0.94 0.94 srgb f gr s n %%%%%% 283 118 m 283 117 l 283 116 l g 284 115 l 284 114 l g 285 113 l 286 112 l 286 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443 99 l g g g g g g g g g g g g i g g g i g g i g g i g i g g i g i g i g i g i i g i g i j i g i i g i i i g i i i g i i i i i i i i i i i 475 133 l i i 474 135 l i 473 136 l i 472 137 l 472 136 l 471 136 l 471 135 l 470 135 l 470 134 l 470 133 l 469 133 l 469 132 l 469 131 l 469 130 l 469 129 l 469 128 l 469 127 l 469 126 l 469 125 l 469 124 l 469 123 l g 470 122 l 470 121 l 470 120 l 470 119 l g 471 118 l 471 117 l g 472 116 l 472 115 l g 473 114 l 473 113 l g 474 112 l 474 111 l g 475 110 l g 476 109 l 477 108 l 477 107 l g 478 106 l g 479 105 l g 481 104 l g 482 103 l g 483 102 l g g 485 101 l g g 487 100 l g g g 490 99 l g g g g g g g g g g g g i g g g i g g i g g i g i g g i g i g i g i g i j i g i g i i g i i g i i i g i i i g i i i i i i i i i i i 522 133 l i i 521 135 l s 521 135 m i 520 136 l i 519 137 l 519 136 l 518 136 l 518 135 l 517 135 l 517 134 l 517 133 l 516 133 l 516 132 l 516 131 l 516 130 l 516 129 l 516 128 l 516 127 l 516 126 l 516 125 l 516 124 l 516 123 l g 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g i i i g i i i i i i i i i i i i 616 134 l i 615 135 l i 614 136 l i 613 137 l 613 136 l 612 136 l 612 135 l 611 135 l 611 134 l 611 133 l 610 133 l 610 132 l 610 131 l 610 130 l 610 129 l 610 128 l 610 127 l 610 126 l 610 125 l 610 124 l 610 123 l g 611 122 l 611 121 l 611 120 l 612 119 l 612 118 l 612 117 l g 613 116 l 613 115 l g 614 114 l 614 113 l g 615 112 l 615 111 l g 616 110 l g 617 109 l g 618 108 l 619 107 l 619 106 l g 620 105 l g 622 104 l g 623 103 l g 625 102 l g 626 101 l g g 628 100 l g g g 631 99 l g g g g g g g g g g g g i g g g i g g i g g i g i g g i g i g i g i g i j i g i g i i g i i g i i j i i i g i i i i i i i i i i i i 663 134 l i 662 136 l 661 136 l i 660 137 l 660 136 l 659 136 l 659 135 l 658 135 l 658 134 l 658 133 l 657 133 l 657 132 l 657 131 l 657 130 l 657 129 l 657 128 l 657 127 l 657 126 l 657 125 l 657 124 l 657 123 l g 658 122 l 658 121 l 658 120 l 659 119 l 659 118 l 659 117 l g 660 116 l 660 115 l g 661 114 l 661 113 l g 662 112 l 662 111 l g 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l 752 132 l 751 132 l 751 131 l 751 130 l 751 129 l 751 128 l 751 127 l 751 126 l 751 125 l 751 124 l g 752 123 l 752 122 l 752 121 l 752 120 l g 753 119 l 753 118 l 753 117 l g 754 116 l 754 115 l g 755 114 l 755 113 l g 756 112 l 756 111 l g 757 110 l g 758 109 l g 759 108 l 760 107 l 760 106 l g 762 105 l g 763 104 l g 764 103 l g 765 102 l g g 767 101 l g g 769 100 l g g g 772 99 l g g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i i g i g i i g i i g i i g i i i j i i i i i i i i i i i i 804 134 l i i 803 136 l 802 136 l i 801 137 l 801 136 l 800 136 l 800 135 l 799 135 l 799 134 l 799 133 l 799 132 l 798 132 l 798 131 l 798 130 l 798 129 l 798 128 l 798 127 l 798 126 l 798 125 l 798 124 l g 799 123 l 799 122 l 799 121 l 799 120 l g 800 119 l 800 118 l 800 117 l g 801 116 l 801 115 l g 802 114 l 802 113 l g 803 112 l 803 111 l g 804 110 l g 805 109 l g 806 108 l 807 107 l 808 106 l g 809 105 l g 810 104 l g 811 103 l g 813 102 l g 814 101 l g g 817 100 l g g 819 99 l g g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i i g i g i i g i i g i i g i i i i g i i i i i i i i i i i i 851 134 l i i 850 136 l 849 136 l i 848 137 l 848 136 l 847 136 l 847 135 l 846 135 l 846 134 l 846 133 l 846 132 l 845 132 l 845 131 l 845 130 l 845 129 l 845 128 l 845 127 l 845 126 l 845 125 l 845 124 l g 846 123 l 846 122 l 846 121 l 846 120 l g 847 119 l 847 118 l 847 117 l g 848 116 l 848 115 l g 849 114 l 849 113 l g 850 112 l 851 111 l 851 110 l g 852 109 l g 853 108 l g 854 107 l 855 106 l g 856 105 l g 857 104 l g 858 103 l g 860 102 l g 861 101 l g g 863 100 l g g g 866 99 l g g g g g g g g g g g g i g g g i g g i g g i g j g i g i g i g i g i g i i g i g i i g i i g i i s n 992 118 m 992 117 l g 993 116 l 993 115 l g 994 114 l g 995 113 l g 996 112 l g 997 111 l g 998 110 l g 999 109 l g g 1001 108 l g 1002 107 l g 1003 106 l g g 1005 105 l g 1007 104 l g 1008 103 l g g 1010 102 l g g g 1013 101 l g g g 1016 100 l g g g g 1020 99 l g g g g g g g g g g g g g g g i g g g g j g g i g g g i g g i g g i g i g g i g i g j g i g i g i g i g i g i g i g i i g i g i i g i g i i g i i g i i g i i g i i i g i i i g i 1073 136 l 1073 135 l g 1074 134 l 1074 133 l 1074 132 l g 1075 131 l 1075 130 l 1075 129 l g 1076 128 l 1076 127 l g 1077 126 l 1077 125 l g 1078 124 l 1078 123 l g 1079 122 l 1079 121 l g 1080 120 l g 1081 119 l g 1082 118 l 1082 117 l g 1083 116 l g 1084 115 l g 1085 114 l g 1086 113 l g 1087 112 l g 1088 111 l g 1089 110 l g 1090 109 l g 1091 108 l g 1092 107 l g g 1094 106 l g 1095 105 l g g 1097 104 l g g 1099 103 l g g 1101 102 l g g 1103 101 l g g g 1106 100 l g g g g 1110 99 l g g g g g g g g g g g g g g g g i g g g g i g g g i g g i g g i g g i g g i g i g g i g i g i g i g i g i g i g i g i g i g i j i g i g i i g i i g i i g i i g i i i g i i i g i i 1163 136 l g 1164 135 l 1164 134 l 1164 133 l g 1165 132 l 1165 131 l 1165 130 l g 1166 129 l 1166 128 l g 1167 127 l 1167 126 l g 1168 125 l 1168 124 l g 1169 123 l 1169 122 l g 1170 121 l g 1171 120 l 1171 119 l g 1172 118 l g 1173 117 l 1174 116 l 1174 115 l g 1175 114 l g 1176 113 l g 1177 112 l g 1178 111 l g 1179 110 l g 1180 109 l g 1182 108 l g 1183 107 l g 1184 106 l g g 1186 105 l g 1187 104 l g g 1189 103 l g g 1191 102 l g g g 1194 101 l g g 1197 100 l g g g g 1201 99 l g g g g g g g g g g g g g g g i g g g g i g g g i g g g i g g i g j g i g g i g i g i g g i g i g i g i g i g i g i i g i g i g i i g i g i i g i i g i i g i i g i i i g i i i g i 1254 136 l 1254 135 l 1254 134 l g 1255 133 l 1255 132 l 1255 131 l g 1256 130 l 1256 129 l g 1257 128 l 1257 127 l g 1258 126 l 1258 125 l g 1259 124 l 1259 123 l g 1260 122 l 1260 121 l g 1261 120 l g 1262 119 l 1262 118 l g 1263 117 l g 1264 116 l g 1265 115 l g 1266 114 l 1267 113 l 1267 112 l g 1269 111 l g 1270 110 l g 1271 109 l g 1272 108 l g 1273 107 l g g 1275 106 l g 1276 105 l g g 1278 104 l g g 1280 103 l g g 1282 102 l g g 1284 101 l g g g 1287 100 l g g g g 1291 99 l g g g g g g g g g g g g g g g g i g g g g i g g g i g g i g g i g g i g g i g i g j g i g i g i g i g i g i g i g i g i g i i g i g i i g i g i i g i i g i i g i i i g i i i g i i 1344 136 l g 1345 135 l 1345 134 l 1345 133 l 1346 132 l 1346 131 l 1346 130 l g 1347 129 l 1347 128 l 1348 127 l 1348 126 l 1348 125 l g 1349 124 l g 1350 123 l 1350 122 l g 1351 121 l 1351 120 l g 1352 119 l g 1353 118 l g 1354 117 l 1354 116 l g 1355 115 l g 1356 114 l g 1357 113 l g 1358 112 l g 1359 111 l g 1360 110 l g 1361 109 l g 1362 108 l g g 1364 107 l g 1365 106 l g g 1367 105 l g 1368 104 l g g 1370 103 l g g 1372 102 l g g 1375 101 l g g 1377 100 l g g g g 1382 99 l g g g g g g g g g g g g g g g i g g g g i g g g i g g i g g g i g i g g i g j g i g i g j g i g i g i g i g i i g i g i g i j i g i i g i g i i g i i g i i i g i i i g i i i g 1435 136 l 1435 135 l 1435 134 l g 1436 133 l 1436 132 l 1436 131 l g 1437 130 l 1437 129 l 1438 128 l 1438 127 l 1438 126 l g 1439 125 l 1439 124 l g 1440 123 l g 1441 122 l 1441 121 l g 1442 120 l 1443 119 l 1443 118 l g 1444 117 l g 1445 116 l g 1446 115 l 1446 114 l g 1447 113 l g 1448 112 l g 1449 111 l g 1450 110 l g 1452 109 l g 1453 108 l g 1454 107 l s 1454 107 m g 1456 106 l g 1457 105 l g g 1459 104 l g 1461 103 l g g 1463 102 l g g 1465 101 l g g g 1468 100 l g g g g 1472 99 l g g g g g g g g g g g g g g g g i g g g g i g g g i g g i g g i g g i g i g g i g i g g i g i g i g i g i g i g i g i g i i g i g i g i i g i i g i g i i g i i i g i i g i i i i g i 1525 136 l 1525 135 l g 1526 134 l 1526 133 l 1526 132 l g 1527 131 l 1527 130 l 1528 129 l 1528 128 l 1528 127 l g 1529 126 l 1529 125 l g 1530 124 l 1530 123 l g 1531 122 l g 1532 121 l 1532 120 l g 1533 119 l g 1534 118 l 1534 117 l g 1535 116 l g 1536 115 l g 1537 114 l g 1538 113 l g 1539 112 l g 1540 111 l g 1541 110 l g 1542 109 l g 1543 108 l g 1545 107 l g 1546 106 l g 1547 105 l g g 1549 104 l g g 1551 103 l g g 1553 102 l g g 1555 101 l g g g 1558 100 l g g g g 1562 99 l g g g g g g g g g g g g g g g g i g g g g i g g g i g g i g g i g g i g g i g i g g i g i g i g i g j g i j i g i g i g i s n 283 826 m i i g i i g i j i g i g i j i g i g i g i g g i g i g g i g g i g g g i g g g g g g g g g g g g 314 844 l g g g 317 843 l g g 319 842 l g g 321 841 l g 322 840 l g 324 839 l g 325 838 l g 326 837 l g 327 836 l 328 835 l 328 834 l g 329 833 l g 330 832 l 331 831 l 331 830 l 332 829 l 332 828 l 333 827 l 333 826 l 333 825 l g 334 824 l 334 823 l 334 822 l 335 821 l 335 820 l 335 819 l 335 818 l 335 817 l 335 816 l 335 815 l 335 814 l 335 813 l 335 812 l 335 811 l 334 811 l 334 810 l 334 809 l 333 809 l 333 808 l 332 808 l 332 807 l 331 807 l i 330 808 l i 329 809 l i i 328 811 l i i i i i i i i i i j i i i g i i j i j i j i g i g i j i g i g i g j g i g i g g i g g i g g g i g g g g g g g g g g g g 361 844 l g g g 364 843 l g g 366 842 l g g 368 841 l g 369 840 l g g 371 839 l g 372 838 l g 373 837 l g 374 836 l 375 835 l 375 834 l g 376 833 l g 377 832 l 378 831 l 378 830 l g 379 829 l 379 828 l 380 827 l 380 826 l 380 825 l g 381 824 l 381 823 l 381 822 l 382 821 l 382 820 l 382 819 l 382 818 l 382 817 l 382 816 l 382 815 l 382 814 l 382 813 l 382 812 l 382 811 l 381 811 l 381 810 l 381 809 l 380 809 l 380 808 l 379 808 l 379 807 l 378 807 l i 377 808 l i 376 809 l i i 375 811 l i i i i i i i i i i g i i i i g i i j i j i g i i g i g i j i g i g i g j g i g i g g i g g i g g g i g g g g g g g g g g g g 408 844 l g g g 411 843 l g g 413 842 l g g 415 841 l g 416 840 l g g 418 839 l g 419 838 l g 420 837 l g 421 836 l g 422 835 l 422 834 l g 423 833 l g 424 832 l 425 831 l 425 830 l g 426 829 l 426 828 l g 427 827 l 427 826 l 427 825 l g 428 824 l 428 823 l 428 822 l g 429 821 l 429 820 l 429 819 l 429 818 l 429 817 l 429 816 l 429 815 l 429 814 l 429 813 l 429 812 l 429 811 l 428 811 l 428 810 l 428 809 l 427 809 l 427 808 l 426 808 l 426 807 l 425 807 l i 424 808 l i 423 809 l i i 422 811 l i i i i i i i i i i g i i i i g i i g i i j i g i i g i g i j i g i g i g j g i g i g g i g g i g g g i g g g g g g g g g g g g 455 844 l g g g 458 843 l g g 460 842 l g g 462 841 l g 463 840 l g g 465 839 l g 466 838 l g 467 837 l g 468 836 l g 469 835 l 469 834 l g 470 833 l g 471 832 l 472 831 l 472 830 l g 473 829 l 473 828 l g 474 827 l 474 826 l 474 825 l g 475 824 l 475 823 l 475 822 l g 476 821 l 476 820 l 476 819 l 476 818 l 476 817 l 476 816 l 476 815 l 476 814 l 476 813 l 476 812 l 476 811 l 475 811 l 475 810 l 475 809 l 474 809 l 474 808 l 473 808 l 473 807 l 472 807 l i 471 808 l i 470 809 l i i 469 811 l i i i i i i i i i i g i i i i g i i g i i g i i g i i g i g i j i g i g i g j g i g i g g i g g i g g g i g g g g g g g g g g g g 502 844 l g g g 505 843 l g g 507 842 l g g 509 841 l g 510 840 l g g 512 839 l g 513 838 l g 514 837 l g 515 836 l g 516 835 l 517 834 l 517 833 l g 518 832 l g 519 831 l 519 830 l g 520 829 l 520 828 l g 521 827 l 521 826 l 521 825 l g 522 824 l s 522 824 m 522 823 l 522 822 l g 523 821 l 523 820 l 523 819 l 523 818 l 523 817 l 523 816 l 523 815 l 523 814 l 523 813 l 523 812 l 523 811 l 522 811 l 522 810 l 522 809 l 521 809 l 521 808 l 520 808 l 520 807 l 519 807 l i 518 808 l i 517 809 l i i 516 811 l i i i i i i i i i i g i i i i g i i g i i g i i g i i g i g i j j i g i g j g i g i g g i g g i g g g i g g g g g g g g g g g g 549 844 l g g g 552 843 l g g 554 842 l g g 556 841 l g 557 840 l g g 559 839 l g 560 838 l g 561 837 l g 562 836 l g 563 835 l 564 834 l 564 833 l g 565 832 l g 566 831 l 566 830 l g 567 829 l 567 828 l g 568 827 l 568 826 l 568 825 l g 569 824 l 569 823 l 569 822 l g 570 821 l 570 820 l 570 819 l 570 818 l 570 817 l 570 816 l 570 815 l 570 814 l 570 813 l 570 812 l 570 811 l 569 810 l 569 809 l 568 809 l 568 808 l 567 808 l 567 807 l 566 807 l i 565 808 l i 564 809 l i i 563 811 l i i i i i i i i i i g i i i i g i i g i i g i i g i i g i g i g i j i g i g g i g i g i g g i g g i g g g i g g g g g g g g g g g g 596 844 l g g g 599 843 l g g 601 842 l g g 603 841 l g 604 840 l g g 606 839 l g 607 838 l g 608 837 l g 609 836 l g 610 835 l 611 834 l 611 833 l g 612 832 l g 613 831 l 613 830 l g 614 829 l 614 828 l g 615 827 l 615 826 l 615 825 l g 616 824 l 616 823 l 616 822 l g 617 821 l 617 820 l 617 819 l 617 818 l 617 817 l 617 816 l 617 815 l 617 814 l 617 813 l 617 812 l 617 811 l 617 810 l 616 810 l 616 809 l 615 809 l 615 808 l 614 808 l 614 807 l 613 807 l i 612 808 l i 611 809 l i i 610 811 l i i i i i i i i i i g i i i j i i g i i g i i g i i g i g i g i j i g i g j g i g j g i g g i g g g i g g g g g g g g g g g g 643 844 l g g g 646 843 l g g 648 842 l g g 650 841 l g 651 840 l g g 653 839 l g 654 838 l g 655 837 l g 656 836 l g 657 835 l 658 834 l 658 833 l g 659 832 l g 660 831 l 660 830 l g 661 829 l 661 828 l g 662 827 l 662 826 l 663 825 l 663 824 l 663 823 l 663 822 l g 664 821 l 664 820 l 664 819 l 664 818 l 664 817 l 664 816 l 664 815 l 664 814 l 664 813 l 664 812 l 664 811 l 664 810 l 663 810 l 663 809 l 662 808 l 661 808 l 661 807 l 660 807 l i 659 808 l i 658 809 l i i 657 811 l i i i i i i i i i i g i i i j i i g i i g i i g i i g i g i g i j j j g i g i g j g i g g i g g g i g g g g g g g g g g g g 690 844 l g g g 693 843 l g g 695 842 l g g 697 841 l g 698 840 l g g 700 839 l g 701 838 l g 702 837 l g 703 836 l g 704 835 l g 705 834 l 705 833 l g 706 832 l g 707 831 l 707 830 l g 708 829 l 708 828 l g 709 827 l 709 826 l 709 825 l g 710 824 l 710 823 l 710 822 l g 711 821 l 711 820 l 711 819 l 711 818 l 711 817 l 711 816 l 711 815 l 711 814 l 711 813 l 711 812 l 711 811 l 711 810 l 710 810 l 710 809 l 709 808 l 708 808 l 708 807 l 707 807 l i 706 808 l i 705 809 l i i 704 812 l s 704 812 m i i i i i i i i j i i i g i i i g i i g i i g i i g i g i g i j j j g i g i g j g i g g i g g g i g g g g g g g g g g g g 737 844 l g g g 740 843 l g g 742 842 l g g 744 841 l g 746 840 l g 747 839 l g 748 838 l g 749 837 l g 750 836 l g 751 835 l g 752 834 l 752 833 l g 753 832 l g 754 831 l 754 830 l g 755 829 l 755 828 l g 756 827 l 756 826 l 757 825 l 757 824 l 757 823 l 757 822 l g 758 821 l 758 820 l 758 819 l 758 818 l 758 817 l 758 816 l 758 815 l 758 814 l 758 813 l 758 812 l 758 811 l 758 810 l 757 810 l 757 809 l 757 808 l 756 808 l 755 808 l 755 807 l 754 807 l i 753 808 l i 752 809 l i i i 751 812 l i i i i i i i i g i i i i g i i i g i i g i i g i i g i g i g i j i g j g i g i g i g g i g g i g g g i g g g g g g g g g g g g 784 844 l g g g 787 843 l g g 789 842 l g g 791 841 l g 793 840 l g 794 839 l g 795 838 l g 796 837 l g 797 836 l g 798 835 l g 799 834 l 799 833 l g 800 832 l g 801 831 l 801 830 l g 802 829 l 802 828 l g 803 827 l 803 826 l g 804 825 l 804 824 l 804 823 l 805 822 l 805 821 l 805 820 l 805 819 l 805 818 l 805 817 l 805 816 l 805 815 l 805 814 l 805 813 l 805 812 l 805 811 l 805 810 l 804 810 l 804 809 l 804 808 l 803 808 l 802 808 l 802 807 l 801 807 l i 800 808 l i 799 809 l i i i 798 812 l i i i i i i i i g i i i i g i i i g i i g i i g i i g i g i g i j j g i g i g i g j g i g g j g g i g g g g g g g g g g g g 831 844 l g g g 834 843 l g g 836 842 l g g 838 841 l g 840 840 l g 841 839 l g 842 838 l g 843 837 l g 844 836 l g 845 835 l g 846 834 l 846 833 l g 847 832 l g 848 831 l 848 830 l g 849 829 l 849 828 l g 850 827 l 850 826 l g 851 825 l 851 824 l 851 823 l 851 822 l g 852 821 l 852 820 l 852 819 l 852 818 l 852 817 l 852 816 l 852 815 l 852 814 l 852 813 l 852 812 l 852 811 l 852 810 l 851 810 l 851 809 l 851 808 l 850 808 l 849 808 l 849 807 l 848 807 l i 847 808 l i 846 809 l i i i 845 812 l i i i i i i i i g i i i i g i i i g i i g i i g i j i g i g i g i j g i g i g i g j g i g g i g g g i g g g g g g g g g g g g 878 844 l g g g 881 843 l g g 883 842 l g g 885 841 l g 887 840 l g 888 839 l g 889 838 l g 890 837 l g 891 836 l g 892 835 l g 893 834 l 893 833 l g 894 832 l g 895 831 l 895 830 l g 896 829 l 896 828 l g 897 827 l 897 826 l s n 992 826 m i g i i g i g i g i g i g i g i g g i g i g i g g i g j g i g g i g g g i g g g i g g g g i g g g g g g g g g g g g g g g 1035 844 l g g g g 1040 843 l g g 1042 842 l g g g 1045 841 l g g 1047 840 l g g 1049 839 l g 1050 838 l g g 1052 837 l g 1053 836 l g 1055 835 l g 1056 834 l g 1057 833 l g 1058 832 l g 1059 831 l g 1060 830 l g 1061 829 l g 1062 828 l g 1063 827 l 1063 826 l g 1064 825 l g 1065 824 l 1065 823 l g 1066 822 l g 1067 821 l 1067 820 l g 1068 819 l 1068 818 l g 1069 817 l 1069 816 l g 1070 815 l 1070 814 l g 1071 813 l 1071 812 l 1071 811 l g 1072 810 l 1072 809 l 1072 808 l g 1073 807 l i i g i i i g i i i g i i g i i g i i g i i g i g i g i i g i g i g i g i g i g i g i g i g i g i g g i g i g g i g g i g g i g g i g g g i g g g g i g g g g g g g g g g g g g g g g 1126 844 l g g g g 1130 843 l g g g 1133 842 l g g 1135 841 l g g 1137 840 l g g 1139 839 l g g 1141 838 l g 1142 837 l g g 1144 836 l g 1145 835 l g 1146 834 l g 1147 833 l g 1148 832 l g 1149 831 l g 1150 830 l g 1151 829 l g 1152 828 l g 1153 827 l g 1154 826 l 1155 825 l 1155 824 l g 1156 823 l g 1157 822 l 1157 821 l g 1158 820 l 1158 819 l g 1159 818 l 1159 817 l g 1160 816 l 1160 815 l g 1161 814 l 1161 813 l 1161 812 l g 1162 811 l 1162 810 l 1162 809 l g 1163 808 l 1163 807 l i g i i i g i i i g i i g i i g i i g i i g i g i i g i g i j i g i g i g i g i g i g i g j g i g i g g i g i g g i g g i g g g i g g j g g g g i g g g g g g g g g g g g g g g 1216 844 l g g g g 1220 843 l g g g 1223 842 l g g g 1226 841 l g g 1228 840 l g 1230 839 l g 1231 838 l g g 1233 837 l g 1234 836 l g 1235 835 l g g 1237 834 l g 1238 833 l g 1239 832 l g 1240 831 l g 1241 830 l g 1242 829 l g 1243 828 l 1243 827 l g 1244 826 l g 1245 825 l g 1246 824 l 1246 823 l g 1247 822 l g 1248 821 l 1248 820 l g 1249 819 l 1249 818 l g 1250 817 l 1250 816 l g 1251 815 l 1251 814 l g 1252 813 l 1252 812 l 1252 811 l g 1253 810 l 1253 809 l 1253 808 l g 1254 807 l i i i g i i i g i i g i i g i i g i i g i i g i g i i g i g i g i g i j i g j g i g i g i g i g g i g i g g i g g i g g i g g i g g g i g g g g i g g g g g g g g g g g g g g g g 1307 844 l g g g g 1311 843 l g g g 1314 842 l g g 1316 841 l g g 1318 840 l g g 1320 839 l g g 1322 838 l g 1323 837 l g 1325 836 l g 1326 835 l g 1327 834 l g 1328 833 l g 1329 832 l g 1330 831 l g 1331 830 l g 1332 829 l g 1333 828 l g 1334 827 l g 1335 826 l 1335 825 l g 1336 824 l g 1337 823 l 1337 822 l g 1338 821 l g 1339 820 l 1339 819 l g 1340 818 l 1340 817 l g 1341 816 l 1341 815 l g 1342 814 l 1342 813 l 1342 812 l g 1343 811 l 1343 810 l 1343 809 l g 1344 808 l 1344 807 l i g i i i j i i g i i j i i g i g i i g i i g i g i g i i g i g i g i g i g i g i g i g i g g i g i g g i g i g g i g g i g g j g g i g g g g j g g g g g g g g g g g g g g g 1397 844 l g g g g 1401 843 l g g g 1404 842 l g g 1406 841 l g g g 1409 840 l g 1410 839 l g g 1412 838 l g 1414 837 l g 1415 836 l g 1416 835 l g 1418 834 l g 1419 833 l g 1420 832 l g 1421 831 l g 1422 830 l g 1423 829 l 1423 828 l g 1424 827 l g 1425 826 l g 1426 825 l 1427 824 l 1427 823 l g 1428 822 l 1428 821 l g 1429 820 l g 1430 819 l 1430 818 l g 1431 817 l 1431 816 l g 1432 815 l 1432 814 l 1432 813 l g 1433 812 l 1433 811 l 1433 810 l g 1434 809 l 1434 808 l 1434 807 l g i i i g i i i g i i j i i g i i g i g i i g i j i g i g i g i i g i g i g i g i g j g i g i g j g i g g i g j g g i g g i g g g i g g g g i g g g g g g g g g g g g g g g g 1488 844 l g g g g 1492 843 l g g g 1495 842 l g g 1497 841 l g g 1499 840 l g g 1501 839 l g 1502 838 l g g 1504 837 l g 1505 836 l g g 1507 835 l g 1508 834 l s 1508 834 m g 1509 833 l g 1510 832 l g 1511 831 l g 1512 830 l g 1513 829 l g 1514 828 l g 1515 827 l 1515 826 l g 1516 825 l g 1517 824 l g 1518 823 l 1518 822 l g 1519 821 l 1519 820 l g 1520 819 l g 1521 818 l 1521 817 l g 1522 816 l 1522 815 l 1522 814 l g 1523 813 l 1523 812 l g 1524 811 l 1524 810 l 1524 809 l 1524 808 l g 1525 807 l i i g i i i g i i j i i g i i g i i g i g i i g i g i i g i g i g i g i g i g i g i g i g i g j g i g i g g i g g i g g i g g i g g g i g g g g i g g g g g g g g g g g g g g g g 1578 844 l g g g g 1582 843 l g g g 1585 842 l g g 1587 841 l g g 1589 840 l g g 1591 839 l g g 1593 838 l g 1594 837 l g g 1596 836 l g 1597 835 l g 1598 834 l g 1599 833 l g 1601 832 l g 1602 831 l 1603 830 l 1603 829 l g 1604 828 l g 1605 827 l g 1606 826 l s n 945 779 m 944 779 l 943 779 l 943 778 l 942 778 l 941 778 l 941 777 l 940 777 l 939 777 l 939 776 l 938 776 l 938 775 l 937 775 l 936 775 l 936 774 l 935 774 l 935 773 l 934 773 l 934 772 l 933 772 l 933 771 l 932 771 l 932 770 l 931 770 l 931 769 l 930 768 l 930 767 l 929 767 l 929 766 l 929 765 l 928 765 l 928 764 l 928 763 l 927 763 l 927 762 l 927 761 l 926 760 l 926 759 l 926 758 l 926 757 l 926 756 l 926 755 l 926 754 l 926 753 l 926 752 l 926 751 l 926 750 l 926 749 l 926 748 l g 927 747 l 927 746 l 927 745 l g 928 744 l 928 743 l g 929 742 l 929 741 l g 930 740 l g 931 739 l 932 738 l 932 737 l g 933 736 l g 934 735 l g 936 734 l g 937 733 l g 938 732 l g g 940 731 l g 942 730 l g g 944 729 l g g 946 728 l g g g g 950 727 l g g g g g g g g g g i g g i g i i i 962 732 l i 961 733 l 960 733 l i 959 734 l 958 734 l 957 734 l 956 734 l 955 734 l 954 734 l 953 734 l 952 734 l 951 734 l 950 734 l 949 734 l 949 733 l 948 733 l 947 733 l 946 733 l 946 732 l 945 732 l 944 732 l 943 732 l 943 731 l 942 731 l 941 731 l 941 730 l 940 730 l 939 730 l 939 729 l 938 729 l 938 728 l 937 728 l 936 728 l 936 727 l 935 727 l 935 726 l 934 726 l 934 725 l 933 725 l 933 724 l 932 724 l 932 723 l 931 723 l 931 722 l 930 721 l 930 720 l 929 720 l 929 719 l 929 718 l 928 718 l 928 717 l 928 716 l 927 716 l 927 715 l 927 714 l 926 713 l 926 712 l 926 711 l 926 710 l 926 709 l 926 708 l 926 707 l 926 706 l 926 705 l 926 704 l 926 703 l 926 702 l 926 701 l g 927 700 l 927 699 l 927 698 l g 928 697 l 928 696 l g 929 695 l 929 694 l g 930 693 l g 931 692 l 931 691 l g 932 690 l g 933 689 l g 934 688 l g 936 687 l g 937 686 l g 938 685 l g g 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954 217 l 953 217 l 952 217 l 951 217 l 950 217 l 950 216 l 949 216 l 948 216 l 947 216 l 946 216 l 946 215 l 945 215 l 944 215 l 944 214 l 943 214 l 942 214 l 941 213 l 940 213 l 940 212 l 939 212 l 938 212 l 938 211 l 937 211 l 937 210 l 936 210 l 935 210 l 935 209 l 934 209 l 934 208 l 933 208 l 933 207 l 932 207 l 932 206 l 931 205 l 931 204 l 930 204 l 930 203 l 929 203 l 929 202 l 929 201 l 928 201 l 928 200 l 928 199 l 927 199 l 927 198 l 927 197 l 927 196 l 926 196 l 926 195 l 926 194 l 926 193 l 926 192 l 926 191 l 926 190 l 926 189 l 926 188 l 926 187 l 926 186 l 926 185 l 926 184 l 927 183 l 927 182 l 927 181 l g 928 180 l 928 179 l g 929 178 l 929 177 l g 930 176 l 930 175 l g 931 174 l g 932 173 l g 933 172 l g 934 171 l g 935 170 l g 936 169 l g g 938 168 l g 939 167 l g g 941 166 l g g 943 165 l g s n 236 826 m n 1653 826 m n 236 118 m n 1653 118 m n 945 826 m n 945 118 m n 118 118 m n 118 826 m n 1771 118 m n 1771 826 m 12 lw n 354 756 m 826 756 33.3333 ato s n 1063 756 m 1535 756 33.3333 ato s n 649 189 m 531 189 33.3333 ato s n 1358 189 m 1240 189 33.3333 ato s 4 lw n 1015 472 m showpage %%EndDocument @endspecial 1206 2932 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1206 2932 a 1189 2954 a Fd(1)1223 2932 y currentpoint grestore moveto 1223 2932 a 2619 2932 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 2619 2932 a 2602 2954 a Fd(2)2635 2932 y currentpoint grestore moveto 2635 2932 a 1206 3638 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1206 3638 a 1189 3660 a Fd(3)1223 3638 y currentpoint grestore moveto 1223 3638 a 2619 3638 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 2619 3638 a 2602 3660 a Fd(4)2635 3638 y currentpoint grestore moveto 2635 3638 a 1913 2932 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1913 2932 a 1896 2954 a Fd(5)1929 2932 y currentpoint grestore moveto 1929 2932 a 1913 3638 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1913 3638 a 1896 3660 a Fd(6)1929 3638 y currentpoint grestore moveto 1929 3638 a 1089 3638 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1089 3638 a 1 1 1 TeXcolorrgb 1 1 1 TeXcolorrgb 728 3687 370 100 v 1 1 1 TeXcolorrgb Black 1 1 1 TeXcolorrgb Black 736 3664 a Fm(T)793 3679 y Fq(3)861 3664 y Fk(=)i(7)p Fm(:)p Fk(0)1089 3638 y currentpoint grestore moveto 1089 3638 a 1089 2932 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1089 2932 a 1 1 1 TeXcolorrgb 1 1 1 TeXcolorrgb 755 2981 342 100 v 1 1 1 TeXcolorrgb Black 1 1 1 TeXcolorrgb Black 763 2958 a Fm(T)820 2973 y Fq(1)888 2958 y Fk(=)g(10)1089 2932 y currentpoint grestore moveto 1089 2932 a 2736 3638 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 2736 3638 a 1 1 1 TeXcolorrgb 1 1 1 TeXcolorrgb 2728 3687 370 100 v 1 1 1 TeXcolorrgb Black 1 1 1 TeXcolorrgb Black 26 x Fm(T)2793 3679 y Fq(4)2861 3664 y Fk(=)g(6)p Fm(:)p Fk(8)3089 3638 y currentpoint grestore moveto 3089 3638 a 2736 2932 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 2736 2932 a 1 1 1 TeXcolorrgb 1 1 1 TeXcolorrgb 2728 2981 370 100 v 1 1 1 TeXcolorrgb Black 1 1 1 TeXcolorrgb Black 26 x Fm(T)2793 2973 y Fq(2)2861 2958 y Fk(=)g(3)p Fm(:)p Fk(6)3089 2932 y currentpoint grestore moveto 3089 2932 a 1983 3285 a gsave currentpoint currentpoint translate 0 neg rotate neg exch neg exch translate 1983 3285 a 1 1 1 TeXcolorrgb 1 1 1 TeXcolorrgb 1975 3337 400 106 v 1 1 1 TeXcolorrgb Black 1 1 1 TeXcolorrgb Black 24 x Fm(\036)2041 3324 y Fq(5)p Ff(!)p Fq(6)2214 3309 y Fk(=)g(0)2366 3285 y currentpoint grestore moveto 2366 3285 a Black 570 3959 a Fu(Figure)e(5:)31 b(The)24 b(lo)n(wer)h(part)f(of)h(the)g(system)f(pumps)f(heat)i(from)g (cold)f(to)h(hot)p Black 640 4079 a Fd(\()p Fq(\000)706 4089 y Fc(i)752 4079 y Fq(=)20 b(1)p Fj(;)11 b(V)934 4088 y Fb(15)1019 4079 y Fq(=)20 b Fj(V)1135 4088 y Fb(56)1219 4079 y Fq(=)g Fj(V)1335 4088 y Fb(36)1420 4079 y Fq(=)f(40)p Fj(;)12 b(V)1637 4088 y Fb(25)1722 4079 y Fq(=)19 b Fj(V)1837 4088 y Fb(46)1922 4079 y Fq(=)h(20)p Fj(;)11 b(\036)2140 4088 y Fb(1)p Fa(!)p Fb(5)2286 4079 y Fq(=)19 b(2)p Fj(:)p Fq(4)p Fj(;)12 b(\036)2524 4088 y Fb(6)p Fa(!)p Fb(3)2669 4079 y Fq(=)20 b(0)p Fj(:)p Fq(2)p Fj(;)11 b(\036)2907 4088 y Fb(5)p Fa(!)p Fb(6)3053 4079 y Fq(=)19 b(0)p Fd(\))p Black 0 4425 a Fu(In)29 b(this)g(last)f(e)o(xample,)i(we)f(construct)g (a)g(system)g(that)f(mimics)g(a)i(thermodynamic)d(heat)j(pump.)43 b(Figure)29 b(5)0 4545 y(sho)n(ws)c(tw)o(o)g(chains)h(of)g(three)g (oscillators)f(coupled)g(through)h(their)f(middle)g(point.)33 b(The)26 b(ends)g(of)g(the)g(upper)0 4666 y(chain)f(are)g(connected)g (to)g(the)g(hottest)e(\()p Fm(T)1446 4681 y Fq(1)1486 4666 y Fu(\))i(and)g(the)g(coldest)f(\()p Fm(T)2257 4681 y Fq(2)2297 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