Content-Type: multipart/mixed; boundary="-------------0302012204125" This is a multi-part message in MIME format. ---------------0302012204125 Content-Type: text/plain; name="03-34.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-34.comments" e-mail : Taku Matsui=matsui@math.kyushu-u.ac.jp, Yoshiko Ogata=ogata@monet.phys.s.u-tokyo.ac.jp ---------------0302012204125 Content-Type: text/plain; name="03-34.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-34.keywords" variational principle; non-equilibrium steady state,the XX model,variational principle, KMS state ---------------0302012204125 Content-Type: application/postscript; name="nessXY2.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="nessXY2.ps" %!PS-Adobe-2.0 %%Creator: dvi2ps %%Title: nessXY2.dvi %%Pages: (atend) %%BoundingBox: 0 0 595 842 %%DocumentPaperSizes: A4 %%Orientation: Portrait %%EndComments %%BeginFile: /usr/local/lib/dvi2ps/dvi2.ps % /TeXDict 300 dict def TeXDict begin /inch { 72 mul } bind def /largepaperarray [ /letter /legal /11x17 /b4 /b5 /a5 /a4 /a3 ] def /smallpaperarray [ /note dup where { pop }{ pop /lettersmall dup where { pop }{ pop /letter } ifelse } ifelse /legal /11x17 /b4 /b5 /a5 /a4small dup where { pop }{ pop /note dup where { pop }{ pop /a4 } ifelse } ifelse /a3 ] def /setpaper { papertray { dup where { exch get exec }{ pop } ifelse }{ pop } ifelse } bind def /trayarray [ /lettertray /legaltray /11x17tray /b4tray /b5tray /a5tray /a4tray /a3tray ] def /settray { dup statusdict exch known manualfeed not and { mark exch statusdict begin load { exec } stopped { $error /newerror get { $error /errorname get /rangecheck eq { (Tray not found, using default tray.\n) print flush TeXDict /papertray false put }{ handleerror } ifelse $error /newerror false put } if } if end cleartomark }{ pop } ifelse } bind def /papertray true def /widtharray [ 8.5 inch 8.5 inch 11 inch 9.84 inch 6.93 inch 5.83 inch 8.27 inch 11.69 inch ] def /heightarray [ 11 inch 14 inch 17 inch 13.9 inch 9.84 inch 8.27 inch 11.69 inch 16.54 inch ] def /xoffset 0 def /yoffset 0 def /leftm 72 def /topm 72 def /landscape false def /manualfeed false def /pagesetup { dup widtharray exch get /paperwidth exch def dup heightarray exch get /paperheight exch def dup trayarray exch get settray large {largepaperarray}{smallpaperarray} ifelse exch get setpaper } bind def /@letter {0 pagesetup} def /@legal {1 pagesetup} def /@tabloid {2 pagesetup} def /@b4 {3 pagesetup} def /@b5 {4 pagesetup} def /@a5 {5 pagesetup} def /@a4 {6 pagesetup} def /@a3 {7 pagesetup} def /@landscape {/landscape true def} bind def /@manualfeed { /manualfeed true def statusdict /manualfeed known { statusdict /manualfeed true put statusdict /manualfeedtimeout 120 put } if } bind def /@large { /large true def } bind def /@small { /large false def } bind def /@envelope { /xoffset 4.28 inch def /yoffset 1.5 inch def @letter } bind def /COPIES { /#copies exch def } bind def /NF { /newname exch def /fsize exch def /corr exch def newname 7 dict def newname load begin /FontType 3 def /FontMatrix [corr 0 0 corr neg 0 0] def /FontBBox [0 0 1 1] def /BitMaps fsize array def /BuildChar /CharBuilder load def /Encoding 256 array def 0 1 255 {Encoding exch /.notdef put} for end newname newname load definefont pop } bind def /ch-image {ch-data 0 get} bind def /ch-width {ch-data 1 get} bind def /ch-height {ch-data 2 get} bind def /ch-xoff {ch-data 3 get} bind def /ch-yoff {ch-data 4 get} bind def /ch-tfmw {ch-data 5 get} bind def /CharBuilder { /ch-code exch def /font-dict exch def /ch-data font-dict /BitMaps get ch-code get def ch-data null eq not { ch-tfmw 0 ch-xoff neg ch-yoff neg ch-width ch-xoff sub ch-height ch-yoff sub setcachedevice ch-width ch-height true [1 0 0 1 ch-xoff ch-yoff] {ch-image} imagemask } if } bind def /BFT { /bf-v exch def /bf-h exch def findfont [bf-h 0 0 bf-v 0 0] makefont def } bind def /BFE 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0 rmoveto } def /s /show load def /ru { /dy exch neg def /dx exch def /x currentpoint /y exch def def newpath x y moveto dx 0 rlineto 0 dy rlineto dx neg 0 rlineto closepath fill x y moveto } bind def /TeXscale { 65781.76 div } def /DocumentInitState [ matrix currentmatrix currentlinewidth currentlinecap currentlinejoin currentdash currentgray currentmiterlimit ] cvx def /startTexFig { /SavedState save def userdict maxlength dict begin currentpoint transform DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix itransform moveto magscale { DVImag dup scale } if /ury exch TeXscale def /urx exch TeXscale def /lly exch TeXscale def /llx exch TeXscale def /y exch TeXscale def /x exch TeXscale def currentpoint /cy exch def /cx exch def /sx x urx llx sub div def /sy y ury lly sub div def sx sy scale cx sx div llx sub cy sy div ury sub translate /DefFigCTM matrix currentmatrix def /initmatrix { DefFigCTM setmatrix } def /defaultmatrix { DefFigCTM exch copy } def /initgraphics { DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix DefFigCTM setmatrix } def /showpage {} def /erasepage {} def /copypage {} def } def /clipFig { currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll exch lineto exch lineto exch lineto closepath clip newpath moveto } def /doclip { llx lly urx ury clipFig } def /endTexFig { end SavedState restore } def /@SpecialDefaults { /hsi paperwidth inch def /vsi paperheight inch def /hof 0 def /vof 0 def /hsc 1 def /vsc 1 def /rotat 0 def /CLIP false def /BBOX false def /EPSF false def /ECL false def } bind def /@ecl {/ECL true def} bind def /@clip {/CLIP true def} bind def /@hsize {/hsi exch def @clip} bind def /@vsize {/vsi exch def @clip} bind def /@hoffset {/hof exch def} bind def /@voffset {/vof exch def} bind def /@scaleunit 1 def /@hscale {@scaleunit div /hsc exch def} bind def /@vscale {@scaleunit div /vsc exch def} bind def /@rotation {/rotat exch def} bind def /@angle /@rotation load def /@rwi {10 div /hsi exch def} bind def /@rhi {10 div /vsi exch def} bind def /@llx {/llx exch def /BBOX true def /hsi 0 def /vsi 0 def} bind def /@lly {/lly exch def} bind def /@urx {/urx exch def} bind def /@ury {/ury exch def} bind def /@bbox {{@clip}if @ury @urx @lly @llx} bind def /@setclipper { CLIP { newpath 0 0 moveto hsi 0 rlineto 0 vsi rlineto hsi neg 0 rlineto closepath clip } if } bind def /@beginspecial { /SpecialSave save def /dict_count countdictstack def /op_count count 1 sub def currentpoint transform initgraphics itransform translate magscale { DVImag dup scale } if landscape {90 rotate} if @SpecialDefaults @MacSetUp } bind def /@setspecial { hof vof translate BBOX { rotat rotate hsi 0 eq { vsi 0 eq { hsc vsc }{ vsi ury lly sub div dup }ifelse }{ vsi 0 eq { hsi urx llx sub div dup }{ hsi urx llx sub div vsi ury lly sub div } ifelse } ifelse scale llx neg ECL{ury}{lly}ifelse neg translate CLIP { newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip } if newpath }{ @setclipper hsc vsc scale rotat rotate } ifelse /CTM matrix currentmatrix def end /letter {} def /note {} def /legal {} def /11x17 {} def /b4 {} def /b5 {} def /a5 {} def /a4 {} def /a4small {} def /a3 {} def /showpage {} def /copypage {} def /erasepage {} def /initmatrix {TeXDict /CTM get setmatrix} bind def /defaultmatrix {TeXDict /CTM get exch copy} bind def /*initclip /initclip load def /initclip { TeXDict begin *initclip matrix currentmatrix CTM setmatrix newpath BBOX { llx lly moveto urx lly lineto urx ury lineto llx ury lineto }{ 0 0 moveto hsi 0 rlineto 0 vsi rlineto hsi neg 0 rlineto } ifelse closepath clip setmatrix end } bind def /initgraphics { initmatrix newpath initclip 1 setlinewidth 0 setlinecap 0 setlinejoin [] 0 setdash 0 setgray 10 setmiterlimit } bind def /languagelevel where { pop languagelevel 1 ne { false setstrokeadjust false setoverprint } if } if } bind def /@MacSetUp { userdict /md known { userdict /md get type /dicttype eq { md /txpose known { md /txpose {pxs pys neg scale} put } if md /cp known { md /cp {pop pop pm restore} put } if } if } if } bind def /@push { gsave currentpoint translate dup scale newpath } bind def /@pop { grestore } bind def /@ar { matrix currentmatrix 7 -2 roll moveto currentpoint translate newpath 5 -2 roll scale 0 0 1 6 -2 roll arc setmatrix } bind def /@RGB /setrgbcolor load def /@HSB /sethsbcolor load def /@CMYK /setcmykcolor dup where { pop load }{ pop { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt {pop 0} if 3 1 roll } repeat setrgbcolor pop } bind } ifelse def /normalscale { Resolution 72 div Resolution 72 div neg scale magscale { DVImag dup scale } if 0 setgray } def end /@endspecial { TeXDict begin count op_count sub {pop} repeat countdictstack dict_count sub {end} repeat SpecialSave restore } bind def /SDict TeXDict def %%EndFile %%BeginFile: /usr/local/lib/dvi2ps/fonts/ascfix-c.ps % This file is included in this dvi2ps (j-version) kit by the courtesy of % Matsushita Electric Industrial Co., Ltd. You are free to distribute this % file as a part of this dvi2ps kit, but if you use this file as a part of % your own program and want to re-distribute the program, you should contact % miyabe@isl.mei.co.jp, kakiuchi@isl.mei.co.jp % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Following procedures are used to define new japanese font which has %%% correct metrics. %%% Added by T.Kakiuchi (kakiuchi@sy6.isl.mei.co.JP) 89/5/19 %%% Copyright (c) Matsushita Electric Industrial Co.,Ltd. 1990 %%% % If the packed-array facility is available, this program sets the % array-packing mode. %systemdict /setpacking known { % /savepacking currentpacking def % true setpacking %} if TeXDict begin % Procedure to make a new font which has new metrics. /Set-New-Metrics % [New-FNam][FNam][Metrics-array] {/Set-Metrics exch def % [New-FNam][FNam] Set-Metrix=[Metrix-Array] findfont % [New-FNam][FDic] /OrigCompFont exch def % [New-FNam] OrigCompFont=[FDic] /NewCompFontName exch def % NewCompFontName=[New-FNam] % Create new composite font. OrigCompFont dup % [FDic][FDic] length dict % [FDic][dict] /NewCompFont exch def % [FDic] NewCompFont=[dict] {1 index % [FDic][key][value][key] /FID ne % [FDic][key][value][T/F] 2 index /UniqueID ne and % [FDic][key][value][T/F] {NewCompFont 3 1 roll put} % if TRUE NewCompFont <- {key,value} {pop pop} ifelse } forall OrigCompFont /FDepVector get % [FDepVector] dup length array % [FDepVector][array] copy % [array] (=[FDepVector]) /NewFDepVector exch def % NewFDepVector=[arrray] NewCompFont /FDepVector NewFDepVector put % [NewCompFont] <- {/FDepVector, NewFDepVector} NewCompFont /FontName NewCompFontName put % [NewCompFont] <- {/FontName, NewCompFontName} Set-Metrics % [code,NewBaseFontName,Metrics-Array] {dup 0 get /Code exch def % set Code dup 1 get /NewBaseFontName exch def % set NewBaseFontName 2 get /Metric-Array exch def % set Metrics-Array % Extract base font and its index to FDepVector. /Index OrigCompFont /Encoding get Code get def /OrigBaseFont NewFDepVector Index get def % Set Metric-Dictionary Metric-Array length dict /Metric-Dict exch def Metric-Dict begin Metric-Array {exec def} forall end % Create new base font. OrigBaseFont dup % [OrgFont][OrgFont] length 2 add % [OrgFont][2+current size] dict % [OrgFont][dict] /NewBaseFont exch def % [OrgFont] /NewBaseFont=[dict] {1 index % [OrgFont][key][value][key] /FID ne % [OrgFont][key][value][T/F] 2 index /UniqueID ne and % [OrgFont][key][value][T/F] {NewBaseFont % [OrgFont][key][value][NewBaseFont] 3 1 roll % [OrgFont][NewBaseFont][key][value] put} % [OrgFont] {pop pop} ifelse } forall NewBaseFont /Kusumi-Metrics Metric-Dict put NewBaseFont % [OrgFont][NewBaseFont] /CDevProc {currentfont /Kusumi-Metrics get exch 2 copy known {get % w0x w0y llx lly urx ury w1x w1y vx vy new-llx dup % w0x w0y llx lly urx ury w1x w1y vx vy new-llx new-llx 8 -1 roll % w0x w0y llx lly ury w1x w1y vx vy new-llx new-llx urx 10 -1 roll % w0x w0y lly ury w1x w1y vx vy new-llx new-llx urx llx sub add % w0x w0y lly ury w1x w1y vx vy new-llx new-urx 7 1 roll % w0x w0y lly new-urx ury w1x w1y vx vy new-llx 8 1 roll % w0x w0y new-llx lly new-urx ury w1x w1y vx vy } {pop pop} ifelse } bind put % Regist to FDepVector NewFDepVector Index NewBaseFontName NewBaseFont definefont put } forall NewCompFontName NewCompFont definefont pop % Define [NewCompFont] as [NewCompFontName] } bind def % Definition of new metrics for /Ryumin-Light-H /Ryumin-Metrics [ [33/Ryumin-Light-H-33[ {/c2B 56.3327 } {/c78 36.5515 } {/c22 127.507 } {/c54 52.5065 } {/c4B 137.007 } {/c39 35.7169 } {/c27 105.323 } {/c42 79.8026 } {/c30 106.905 } {/c6B 129.961 } {/c50 192.016 } {/c47 101.333 } {/c59 104.456 } {/c35 124.507 } {/c3E 51.8327 } {/c2C 81.7527 } {/c23 102.007 } {/c4E 132.007 } {/c2A 111.833 } {/c43 153.333 } {/c55 52.5065 } {/c4A 137.007 } {/c26 106.333 } {/c51 192.017 } {/c2D 73.195 } {/c46 101.833 } {/c58 104.457 } {/c6A 53.6868 } {/c71 162.717 } {/c68 12.747 } {/c56 87.0065 } {/c4D 120.007 } {/c29 50.4616 } {/c52 99.5065 } {/c5B 122.007 } {/c37 145.717 } {/c6D 73.5612 } {/c49 95.824 } {/c2E 73.1949 } {/c72 45.6719 } {/c25 106.833 } {/c69 33.1968 } {/c70 147.722 } {/c57 87.0065 } {/c33 123.507 } {/c53 99.5065 } {/c28 101.333 } {/c4C 120.007 } {/c2F 86.4865 } {/c48 95.6039 } {/c5A 122.007 } {/c6C 154.132 } {/c36 154.717 } {/c24 103.833 } {/c4F 131.507 } ]] [36/Ryumin-Light-H-36[ {/c30 154.133 } {/c27 97.2168 } {/c39 76.6303 } {/c23 76.1769 } {/c67 149.762 } {/c43 67.7751 } {/c6E 77.4092 } {/c31 105.385 } {/c63 75.9087 } {/c26 241.525 } {/c6A 273.126 } {/c29 82.2642 } {/c32 65.1122 } {/c25 184.155 } {/c21 83.9483 } {/c65 90.2671 } {/c3A 51.3751 } {/c2F 295.128 } ]] [37/Ryumin-Light-H-37[ {/c22 140.608 } {/c6F 163.078 } {/c30 99.7332 } {/c27 57.7171 } {/c42 59.748 } {/c47 67.1082 } {/c35 83.0882 } {/c3E 72.1387 } {/c23 138.672 } {/c67 152.293 } {/c4E 197.608 } {/c2A 134.608 } {/c43 117.717 } {/c6E 126.697 } {/c31 115.108 } {/c55 168.068 } {/c63 80.217 } {/c4A 116.233 } {/c26 162.618 } {/c75 124.712 } {/c3F 192.108 } {/c46 123.608 } {/c6A 239.098 } {/c5F 258.608 } {/c44 162.608 } {/c56 84.1834 } {/c29 108.717 } {/c76 83.6869 } {/c32 61.9606 } {/c64 109.108 } {/c49 202.688 } {/c25 122.757 } {/c72 193.323 } {/c40 110.209 } {/c69 178.108 } {/c45 91.8148 } {/c57 89.1683 } {/c21 107.237 } {/c65 49.507 } {/c2F 187.108 } {/c41 97.8211 } {/c48 277.108 } {/c36 51.291 } {/c61 191.608 } {/c24 186.108 } {/c3D 164.236 } ]] ] def % Definition of new metrics for /GothicBBB-Medium-H /Gothic-Metrics [ [33/GothicBBB-Medium-H-33[ {/c2B 62.8327 } {/c78 11.5265 } {/c22 129.507 } {/c54 58.5065 } {/c4B 136.007 } {/c39 14.7171 } {/c27 104.333 } {/c42 76.8826 } {/c30 110.507 } {/c6B 138.987 } {/c50 178.072 } {/c47 104.833 } {/c59 107.036 } {/c35 67.0065 } {/c3E -13.1673 } {/c2C 78.8429 } {/c23 98.9866 } {/c4E 132.507 } {/c2A 132.288 } {/c43 149.333 } {/c55 58.5065 } {/c4A 136.007 } {/c26 102.833 } {/c51 177.982 } {/c2D 55.8326 } {/c46 104.333 } {/c58 107.037 } {/c6A 43.6568 } {/c71 130.717 } {/c68 5.70184 } {/c56 93.5065 } {/c4D 120.007 } {/c29 81.9568 } {/c52 97.5065 } {/c5B 121.007 } {/c37 148.717 } {/c6D 75.5065 } {/c49 56.9765 } {/c2E 55.8327 } {/c72 101.717 } {/c25 102.833 } {/c69 20.1768 } {/c70 109.182 } {/c57 94.0065 } {/c33 76.5065 } {/c53 97.5065 } {/c28 104.333 } {/c4C 120.007 } {/c2F 102.506 } {/c48 56.0265 } {/c5A 121.007 } {/c6C 157.007 } {/c36 133.717 } {/c24 105.833 } {/c4F 132.507 } ]] [36/GothicBBB-Medium-H-36[ {/c30 154.608 } {/c27 97.2418 } {/c39 93.5732 } {/c23 58.2168 } {/c67 106.287 } {/c43 51.2172 } {/c6E 71.752 } {/c31 128.098 } {/c63 52.2169 } {/c26 207.583 } {/c6A 211.098 } {/c29 51.7468 } {/c32 69.0981 } {/c25 155.272 } {/c21 86.707 } {/c65 84.167 } {/c3A 70.6131 } {/c2F 256.108 } ]] [37/GothicBBB-Medium-H-37[ {/c22 82.6082 } {/c6F 135.608 } {/c30 91.1081 } {/c27 74.2168 } {/c42 55.1081 } {/c47 49.6081 } {/c35 87.1181 } {/c3E 83.6081 } {/c23 102.766 } {/c67 113.717 } {/c4E 163.334 } {/c2A 111.608 } {/c43 84.5454 } {/c6E 96.2168 } {/c31 77.6081 } {/c55 140.608 } {/c63 67.7169 } {/c4A 75.6082 } {/c26 149.118 } {/c75 110.257 } {/c3F 144.608 } {/c46 96.6082 } {/c6A 225.578 } {/c5F 215.108 } {/c44 117.481 } {/c56 91.1081 } {/c29 72.2168 } {/c76 63.2168 } {/c32 48.6081 } {/c64 96.6081 } {/c49 209.108 } {/c25 104.207 } {/c72 165.608 } {/c40 76.6081 } {/c69 129.108 } {/c45 72.1081 } {/c57 64.6481 } {/c21 47.2171 } {/c65 41.7168 } {/c2F 135.608 } {/c41 97.6082 } {/c48 262.608 } {/c36 52.1181 } {/c61 188.976 } {/c24 148.446 } {/c3D 123.059 } ]] ] def end % TeXDict %systemdict /setpacking known { % savepacking setpacking %} if %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%EndFile %%EndProlog %%BeginSetup %%PaperSize: A4 %%Feature: *ManualFeed False %%Feature: *Resolution 400 TeXDict begin @large @a4 1.000 100 /f0 NF f0 SF [<000800100020006000C001C0018003800300070006000E000E001C001C003C0038003800380078007800780078007000F000 F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000700078007800780078003800380038003C00 1C001C000E000E000600070003000380018001C000C00060002000100008> 16 65 -9 63 25.367] 0 D 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f17 SF 343 2390 p (Lemma)s 21 r (4.2)s f13 SF 28 r (Supp)s -2 r (ose)s 15 r (that)s 15 r (ther)s -2 r (e)s 15 r (exists)s 15 r (a)s 16 r (one-p)s -2 r (ar)s -3 r (ameter)s 15 r (gr)s -2 r (oup)s 14 r (of)s 16 r (automorphisms)s 343 2457 p (of)s f19 SF 18 r (A)s f5 SF 446 2465 p (S)s f6 SF 497 2457 p (\013)s f5 SF 532 2437 p (S)s f13 SF 582 2457 p (such)s 19 r (that)s f6 SF 18 r (!)s f13 SF 20 r (is)s f3 SF 18 r (\()s f6 SF (\013)s f5 SF 988 2437 p (S)s f6 SF 1020 2457 p (;)s 9 r (\014)s f3 SF 3 r (\))s f13 SF (-KMS)s 18 r (state.)s 25 r (Then,)s f6 SF 18 r (\013)s f5 SF 1612 2437 p (S)s 1612 2471 p (t)s f9 SF 1653 2457 p (\016)s f3 SF 9 r (\002)s 15 r (=)s 15 r (\002)s f9 SF 9 r (\016)s f6 SF 9 r (\013)s f5 SF 1930 2437 p (S)s 1930 2471 p (t)s f13 SF 1962 2457 p (,)s 18 r (and)s f6 SF 19 r (\013)s f5 SF 2139 2437 p (S)s 2139 2471 p (t)s f9 SF 2171 2457 p (j)s f20 SF 2186 2465 p (A)s f1 SF 2219 2471 p (+)s f13 SF 343 2523 p (is)s 20 r (given)s 20 r (by)s f6 SF 915 2631 p (\013)s f5 SF 951 2609 p (S)s 951 2645 p (t)s f3 SF 983 2631 p (\()s f6 SF (a)s f8 SF 1034 2609 p (\003)s f3 SF 1059 2631 p (\()s f6 SF (f)s f3 SF 6 r (\))s f6 SF (a)s f3 SF (\()s f6 SF (g)s f3 SF 2 r (\)\))s 15 r (=)s f6 SF 16 r (a)s f8 SF 1361 2609 p (\003)s f3 SF 1386 2631 p (\()s f6 SF (u)s f5 SF 1439 2640 p (t)s f6 SF 1459 2631 p (f)s f3 SF 6 r (\))s f6 SF (a)s f3 SF (\()s f6 SF (u)s f5 SF 1596 2640 p (t)s f6 SF 1615 2631 p (g)s f3 SF 2 r (\))s f6 SF (:)s f13 SF 343 2740 p (pr)s -2 r (o)s -3 r (of)s f3 SF 343 2806 p (By)s 20 r (the)s 20 r (de\014nition)s 20 r (of)s f6 SF 20 r (!)s f3 SF 2 r (,)s f6 SF 21 r (!)s f9 SF 15 r (\016)s f3 SF 13 r (\002)s 18 r (=)s f6 SF 18 r (!)s f3 SF 2 r (.)s 30 r (As)s f6 SF 20 r (!)s f3 SF 22 r (is)s f6 SF 20 r (\013)s f5 SF 1440 2786 p (S)s f3 SF 1472 2806 p (-KMS)s 20 r (state,)s f6 SF 20 r (!)s f9 SF 16 r (\016)s f6 SF 13 r (\013)s f5 SF 1914 2786 p (S)s f3 SF 1964 2806 p (=)s f6 SF 18 r (!)s f3 SF 2 r (.)s 30 r (Hence)s 343 2872 p (\002)s 24 r (and)s f6 SF 25 r (\013)s f5 SF 559 2852 p (S)s f3 SF 616 2872 p (are)s 24 r (b)s 2 r (oth)s 24 r (extendible)s 24 r (to)s 24 r (the)s 25 r (v)s -1 r (on)s 23 r (Neumann)s 25 r (algebra)s f6 SF 24 r (\031)s f2 SF 1898 2881 p (^)s f5 SF -24 r (!)s f3 SF 1927 2872 p (\()s f19 SF (A)s f5 SF 1988 2852 p (S)s f3 SF 2020 2872 p (\))s f7 SF 2042 2836 p (00)s f3 SF 2072 2872 p (,)s 25 r (which)s 343 2939 p (we)s 22 r (denote)s 23 r (b)s -1 r (y)s 23 r (the)s 23 r (same)s 23 r (sym)s -1 r (b)s 1 r (ol)s 23 r (and)s f6 SF 23 r (!)s f3 SF 26 r (is)s 23 r (\()s 5 r (^)s f6 SF -32 r (\013)s f5 SF 1421 2919 p (S)s f6 SF 1453 2939 p (;)s 9 r (\014)s f3 SF 3 r (\)-KMS)s 24 r (state)s 23 r (on)s f6 SF 23 r (\031)s f2 SF 1957 2947 p (^)s f5 SF -25 r (!)s f3 SF 1985 2939 p (\()s f19 SF (A)s f5 SF 2046 2919 p (S)s f3 SF 2079 2939 p (\))s f7 SF 2100 2902 p (00)s f3 SF 2130 2939 p (.)s 39 r (By)s 343 3005 p (Lemma)s 26 r (4.1,)s f6 SF 28 r (!)s f3 SF 28 r (is)s 25 r (faithful)s 26 r (for)s f6 SF 26 r (\031)s f2 SF 1116 3014 p (^)s f5 SF -25 r (!)s f3 SF 1144 3005 p (\()s f19 SF (A)s f5 SF 1205 2985 p (S)s f3 SF 1237 3005 p (\))s f7 SF 1259 2969 p (00)s f3 SF 1289 3005 p (.)s 47 r (By)s 25 r (the)s 26 r (uniqueness)s 26 r (of)s 26 r (automorphism)s 343 3072 p (which)s 19 r (mak)s -1 r (es)s 20 r (a)s 20 r (faithful)s 21 r (state)s 20 r (on)s 21 r (v)s -1 r (on)s 19 r (Neumann)s 21 r (algebra)s 20 r (b)s 2 r (e)s 20 r (a)s 21 r (KMS)s 20 r (state,)s 21 r ([7])s 20 r (we)s 343 3138 p (obtain)s f6 SF 24 r (\013)s f5 SF 556 3146 p (t)s f9 SF 592 3138 p (\016)s f3 SF 16 r (\002)s 25 r (=)s 25 r (\002)s f9 SF 16 r (\016)s f6 SF 16 r (\013)s f5 SF 910 3146 p (t)s f3 SF 930 3138 p (.)s 41 r (Hence)s f6 SF 25 r (\013)s f9 SF (j)s f20 SF 1208 3146 p (A)s f1 SF 1240 3152 p (+)s f3 SF 1299 3138 p (giv)s -1 r (es)s 23 r (an)s 24 r (automorphism)s 25 r (of)s f19 SF 24 r (A)s f2 SF 2003 3146 p (+)s f3 SF 2040 3138 p (,)s 25 r (and)s 25 r (b)s -1 r (y)s 343 3205 p (restriction,)s f6 SF 22 r (!)s f9 SF 2 r (j)s f20 SF 679 3213 p (A)s f1 SF 711 3218 p (+)s f3 SF 766 3205 p (is)s f6 SF 21 r (\013)s f9 SF 15 r (\000)s f6 SF 14 r (K)s 4 r (M)s 6 r (S)s f3 SF 24 r (state)s 21 r (of)s f19 SF 21 r (A)s f3 SF (.)s 33 r (On)s 21 r (the)s 21 r (other)s 22 r (hands,)s f6 SF 21 r (!)s f3 SF 24 r (satis\014es)s 21 r (the)s 343 3271 p (KMS)s 14 r (condition)s 13 r (with)s 14 r (the)s 13 r (automorphism)s 14 r (giv)s -1 r (en)s 13 r (b)s -1 r (y)s f6 SF 13 r (\013)s f8 SF 1540 3251 p (0)s f3 SF 1555 3271 p (\()s f6 SF (a)s f8 SF 1606 3251 p (\003)s f3 SF 1631 3271 p (\()s f6 SF (f)s f3 SF 6 r (\))s f6 SF (a)s f3 SF (\()s f6 SF (g)s f3 SF 2 r (\)\))s 16 r (=)s f6 SF 15 r (a)s f8 SF 1933 3251 p (\003)s f3 SF 1958 3271 p (\()s f6 SF (u)s f5 SF 2011 3279 p (t)s f6 SF 2031 3271 p (f)s f3 SF 6 r (\))s f6 SF (a)s f3 SF (\()s f6 SF (u)s f5 SF 2168 3279 p (t)s f6 SF 2187 3271 p (g)s f3 SF 2 r (\).)s 343 3337 p (As)s f6 SF 19 r (!)s f9 SF 2 r (j)s f20 SF 477 3346 p (A)s f1 SF 509 3351 p (+)s f3 SF 562 3337 p (is)s 18 r 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596 p (2)s f3 SF 671 583 p (+)s f6 SF 12 r (a)s f2 SF 756 591 p (2)s f13 SF 780 583 p (.)s 26 r (Then)s 20 r (we)s 19 r (have)s f6 SF 636 700 p (V)s f5 SF 668 708 p (t)s f6 SF 687 700 p (QV)s f8 SF 776 677 p (\003)s f5 SF 763 713 p (t)s f3 SF 816 700 p (=)s f6 SF 16 r (\013)s f5 SF 911 677 p (S)s 910 713 p (t)s f9 SF 955 700 p (\016)s f3 SF 12 r (\000)s f9 SF 12 r (\016)s f3 SF 13 r (\002)s f8 SF 1125 708 p (\000)s f9 SF 1174 700 p (\016)s f3 SF 13 r (\000)s f9 SF 12 r (\016)s f6 SF 12 r (\013)s f5 SF 1337 676 p (S)s f8 SF 2 r (\000)s f2 SF (1)s f5 SF 1337 713 p (t)s f9 SF 1438 700 p (\016)s f3 SF 12 r (\002)s f8 SF 1521 708 p (\000)s f3 SF 1558 700 p (\()s f6 SF (Q)s f3 SF (\))s f6 SF (;)s f9 SF 66 r (8)s f6 SF (Q)s f9 SF 15 r (2)s f19 SF 16 r (A)s f2 SF 1908 708 p (+)s f6 SF 1945 700 p (:)s f13 SF 343 817 p (wher)s -2 r (e)s f3 SF 19 r (\000\()s f6 SF (Q)s f3 SF (\))s 15 r (=)s f6 SF 16 r (B)s f2 SF 737 825 p (2)s f6 SF 761 817 p (QB)s f8 SF 850 793 p (\000)s f2 SF (1)s 847 831 p 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1749 p (')s f5 SF 720 1757 p (q)s f3 SF 745 1749 p (\()s f6 SF (V)s f5 SF 798 1757 p (t)s f6 SF 818 1749 p (AV)s f8 SF 904 1726 p (\003)s f5 SF 892 1763 p (t)s f3 SF 929 1749 p (\))s 16 r (=)s f6 SF 15 r (')s f5 SF 1061 1757 p (q)s f3 SF 1085 1749 p (\()s f6 SF (\013)s f5 SF 1143 1726 p (S)s 1142 1763 p (t)s f9 SF 1187 1749 p (\016)s f3 SF 12 r (\000)s f9 SF 13 r (\016)s f3 SF 12 r (\002)s f8 SF 1357 1757 p (\000)s f9 SF 1406 1749 p (\016)s f3 SF 13 r (\000)s f9 SF 12 r (\016)s f6 SF 12 r (\013)s f5 SF 1569 1726 p (S)s f8 SF 2 r (\000)s f2 SF (1)s f5 SF 1569 1763 p (t)s f9 SF 1670 1749 p (\016)s f3 SF 12 r (\002)s f8 SF 1753 1757 p (\000)s f3 SF 1790 1749 p (\()s f6 SF (A)s f3 SF (\)\))s f6 SF (:)s f3 SF 343 1866 p (Then)s 18 r (w)s -1 r (e)s 17 r (conclude)s 18 r (that)s f6 SF 18 r (')s f5 SF 950 1874 p (q)s f3 SF 975 1866 p (\()s f6 SF (V)s f5 SF 1028 1874 p (t)s f9 SF 1059 1866 p (\001)s f6 SF 11 r (V)s f8 SF 1130 1846 p (\003)s f5 SF 1117 1880 p (t)s f3 SF 1155 1866 p (\))s 18 r (is)s 18 r (quasifree,)s 18 r (whic)s -1 r (h)s 17 r (is)s 18 r (giv)s -1 r (en)s 17 r (b)s -1 r (y)s 17 r (the)s 18 r (t)s -1 r (w)s -1 r (o)s 17 r (p)s 1 r (oint)s 343 1933 p (function)s f6 SF 889 2050 p (')s f5 SF 926 2058 p (q)s f3 SF 950 2050 p (\()s f6 SF (V)s f5 SF 1004 2058 p (t)s f6 SF 1023 2050 p (a)s f8 SF 1053 2027 p (\003)s f3 SF 1078 2050 p (\()s f6 SF (f)s f3 SF 6 r (\))s f6 SF (a)s f3 SF (\()s f6 SF (g)s f3 SF 2 r (\))s f6 SF (V)s f8 SF 1299 2027 p (\003)s f5 SF 1287 2063 p (t)s f3 SF 1325 2050 p (\))s 15 r (=)s f9 SF 16 r (h)s f6 SF (w)s f5 SF 1481 2058 p (t)s f6 SF 1501 2050 p (f)s 3 r (;)s 9 r (q)s 2 r (w)s f5 SF 1622 2058 p (t)s f6 SF 1641 2050 p (g)s f9 SF 2 r (i)s f6 SF (:)s f3 SF 343 2167 p (where)s f6 SF 27 r (S)s f3 SF 32 r (=)s f6 SF 29 r (P)s f2 SF 685 2175 p (+)s f9 SF 740 2167 p (\000)s f6 SF 18 r (P)s f8 SF 836 2175 p (\000)s f3 SF 874 2167 p (,)s f6 SF 28 r (w)s f5 SF 957 2175 p (t)s f3 SF 1006 2167 p (=)s f6 SF 29 r (u)s f5 SF 1110 2175 p (t)s f6 SF 1129 2167 p (S)s 4 r (u)s f8 SF 1198 2175 p (\000)s f5 SF (t)s f6 SF 1252 2167 p (S)s f3 SF 3 r (.)s 50 r (It)s 26 r (is)s 27 r (generally)s 27 r (kno)s -1 r (wn)s 26 r (that)s 27 r (an)s 26 r (auto-)s 343 2233 p (morphism)s 20 r (which)s 19 r (maps)s 21 r (an)s -1 r (y)s 19 r (quasifree)s 21 r (state)s 20 r (to)s 20 r (a)s 21 r (quasifree)s 20 r (state)s 21 r (is)s 20 r (a)s 20 r (Bogoliub)s 2 r (o)s -1 r (v)s 343 2299 p (automorphism.)s 24 r (It)s 17 r (turns)s 17 r (out)s 17 r (that)s 17 r (there)s 17 r (exists)s 17 r (a)s 17 r (one)s 16 r (parameter)s 17 r (family)s 17 r (of)s 17 r (unitary)s 343 2366 p (op)s 2 r (erators)s f6 SF 18 r (v)s f5 SF 615 2374 p (t)s f3 SF 653 2366 p (suc)s -1 r (h)s 18 r (that)s f6 SF 1048 2483 p (V)s f5 SF 1081 2491 p (t)s f6 SF 1100 2483 p (B)s f3 SF 3 r (\()s f6 SF (f)s f3 SF 6 r (\))s f6 SF (V)s f8 SF 1266 2460 p (\003)s f5 SF 1253 2496 p (t)s f3 SF 1306 2483 p (=)s f6 SF 16 r (B)s f3 SF 3 r (\()s f6 SF (v)s f5 SF 1458 2491 p (t)s f6 SF 1477 2483 p (f)s 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(t)s 18 r (handside)s 343 2707 p (is)s 15 r (in\014nite.)s 24 r (This)s 15 r (is)s 15 r (a)s 15 r (con)s -1 r (tradiction)s 14 r (and)s 15 r (we)s 14 r (conclude)s 15 r (that)s 15 r (1)s f9 SF 5 r (\000)s f6 SF 6 r (u)s f5 SF 1791 2715 p (t)s f6 SF 1810 2707 p (S)s 3 r (u)s f8 SF 1879 2715 p (\000)s f5 SF (t)s f6 SF 1933 2707 p (S)s f3 SF 18 r (is)s 15 r (not)s 15 r (trace)s 343 2773 p (class.)s 426 2906 p (As)s 19 r (a)s 18 r (consequence,)s 19 r (w)s -1 r (e)s 17 r (obtain)s 19 r (the)s 18 r (following)s 17 r (Theorem,)s f17 SF 343 3017 p (Theorem)s 21 r (4.1)s f13 SF 28 r (The)s 16 r (non-e)s -1 r (quilibrium)s 15 r (ste)s -2 r (ady)s 16 r (state)s f6 SF 16 r (!)s f13 SF 18 r (of)s 17 r (the)s 16 r (XX)s 17 r (mo)s -2 r (del)s f6 SF 15 r (!)s f13 SF 19 r (c)s -2 r (annot)s 15 r (b)s -2 r (e)s 343 3083 p (a)s 20 r (KMS)s 20 r (state)s 20 r (of)s 19 r (any)s 20 r (one-p)s -2 r (ar)s -3 r (ameter)s 19 r (gr)s -2 r (oup)s 19 r (automorphism)s 20 r (of)s 20 r (the)s f6 SF 20 r (C)s f8 SF 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SF 472 470 p ([1])s 28 r (H.Araki,)s f13 SF (On)s 25 r (quasifr)s -2 r (e)s -3 r (e)s 24 r (states)s 25 r (of)s f3 SF 26 r (CAR)s f13 SF 25 r (and)s 25 r (Bo)s -2 r (goliub)s -3 r (ov)s 24 r (automorphisms.)s f3 SF 558 536 p (Publ.)s 19 r (Res.)s 18 r (Inst.)s 19 r (Math.)s 18 r (Sci.)s f17 SF 19 r (6)s f3 SF 18 r (385-442,)s 19 r (\(1970/71\))s 472 647 p ([2])s 28 r (H.Araki,)s f13 SF (On)s 34 r (the)s 35 r (e)s -2 r (quivalenc)s -3 r (e)s 33 r (of)s 35 r (the)s 34 r (KMS)s 34 r (c)s -2 r (ondition)s 34 r (and)s 34 r (the)s 34 r (varia-)s 558 713 p (tional)s 23 r (princip)s -2 r (al)s 21 r (for)s 22 r (quantum)s 22 r (lattic)s -2 r (e)s 22 r (systems)s f3 SF 21 r (Commn.Math.Ph)s -1 r (ys.)s f17 SF (38)s f3 SF (,1-)s 558 780 p (10,\(1974\))s 472 891 p ([3])s 28 r (H.)s 75 r (Araki,)s f13 SF (On)s 72 r (the)s f6 SF 71 r (X)s 5 r (Y)s f13 SF 12 r (-mo)s -2 r (del)s 71 r (on)s 71 r (two-side)s -1 r (d)s 70 r (in\014nite)s 72 r (chain)s f3 SF 558 957 p (Publ.RIMS,Kyoto)s 17 r (Univ,)s f17 SF 19 r (20)s f3 SF 18 r (277)s 19 r (\(1984\).)s 472 1068 p ([4])s 28 r (Huzihiro)s 18 r (Araki)s 19 r (and)s 18 r (Ha)s 4 r (jime)s 18 r (Moriya,)s f13 SF 17 r (Equilibrium)s 20 r (Statistic)s -2 r (al)s 19 r (Me)s -2 r (chanics)s 558 1134 p (of)s 20 r (F)s -3 r (ermion)s 19 r (L)s -2 r (attic)s -3 r (e)s 19 r (Systems)s 20 r (math-ph/0211016)s f3 SF 472 1245 p ([5])s 28 r (W.H.)s 21 r (Asch)s -2 r (bac)s -1 r (her)s 20 r (C.-A.)s 21 r (Pillet)s 21 r (,)s f13 SF 22 r (Non-Equilibrium)s 22 r (Ste)s -2 r (ady)s 22 r (States)s 22 r (of)s 22 r (the)s 558 1311 p (XY)s 20 r (Chain)s f3 SF 19 r (mp-arc)s 18 r (/02-459)s 19 r (,\(2002\).)s 472 1422 p ([6])s 28 r (O.)s 16 r (Bratteli)s 16 r (and)s 15 r (D.)s 16 r (W.)s 16 r (Robinson,)s f13 SF 16 r (Op)s -1 r (er)s -3 r (ator)s 16 r (Algebr)s -3 r (as)s 16 r (and)s 18 r (Quantum)s 17 r (Sta-)s 558 1488 p (tistic)s -1 r (al)s 18 r (Me)s -1 r (chanics)s 18 r (1)s f3 SF (,)s 19 r (Springer-V)s -4 r (erlag,)s 18 r (1987.)s 472 1599 p ([7])s 28 r (O.)s 16 r (Bratteli)s 16 r (and)s 15 r (D.)s 16 r (W.)s 16 r (Robinson,)s f13 SF 16 r (Op)s -1 r (er)s -3 r (ator)s 16 r (Algebr)s -3 r (as)s 16 r (and)s 18 r (Quantum)s 17 r (Sta-)s 558 1665 p (tistic)s -1 r (al)s 18 r (Me)s -1 r (chanics)s 18 r (2)s f3 SF (,)s 19 r (Springer-V)s -4 r (erlag,)s 18 r (1996.)s 472 1776 p ([8])s 28 r (Juerg)s 19 r (F)s -3 r (roehlich,)s 18 r (Marco)s 20 r (Merkli,)s 19 r (Daniel)s 20 r (Ueltsc)s -1 r (hi)s f13 SF 18 r (Dissip)s -1 r (ative)s 19 r (T)s -3 r (r)s -3 r (ansp)s -3 r (ort:)s 558 1843 p (Thermal)s 20 r (Contacts)s 19 r (and)s 19 r (T)s -4 r (unnel)s 2 r (ling)s 19 r (Junctions.)s f3 SF 18 r (preprint,)s 16 r (mp-arh/02-528)s 558 1909 p (,)s 19 r (2002.)s 472 2020 p ([9])s 28 r (Haag,R,)s 21 r (Kastler,D.)s 22 r (and)s 21 r (T)s -4 r (ryc)s -1 r (h-P)s -2 r (ohlmey)s -1 r (er,)s 21 r (E.B.,)s f13 SF 22 r (Stability)s 23 r (and)s 22 r (e)s -2 r (quilib-)s 558 2086 p (rium)s 20 r (states.)s f3 SF 19 r (Comm.)s 18 r (Math.)s 19 r (Ph)s -1 r (ys.)s f17 SF 17 r (38)s f3 SF 19 r (\(1974\),)s 18 r (173{193.)s 445 2197 p ([10])s 27 r (T.G.Ho,andH.Araki,)s f13 SF (Asymptotic)s 17 r (time)s 17 r (evolution)s 16 r (of)s 17 r (a)s 17 r (p)s -2 r (artitione)s -3 r (d)s 16 r (in\014nite)s 558 2263 p (two-side)s -1 r (d)s 18 r (isotr)s -1 r (opic)s f6 SF 18 r (X)s 5 r (Y)s f13 SF 12 r (-chain)s f3 SF 18 r (Pro)s 2 r (c.Steklo)s -1 r (vInst.Math,\(2000\).)s 445 2374 p ([11])s 27 r (V)s -3 r (o)s 2 r (jk)s -2 r (an)s 17 r (Jaksic)s 19 r (,)s 19 r (C.-A.)s 19 r (Pillet)s f13 SF 18 r (On)s 20 r (entr)s -1 r (opy)s 19 r (pr)s -2 r (o)s -3 r (duction)s 19 r (in)s 20 r (quantum)s 20 r (statis-)s 558 2440 p (tic)s -1 r (al)s 18 r (me)s -1 r (chanics.)s f3 SF 17 r (Commn.Math.Ph)s -1 r (ys.)s f17 SF (217)s f3 SF (,285-293,\(2001\).)s 445 2551 p ([12])s 27 r (V.)s 18 r (Jaksic,)s 18 r (C.-A.)s 18 r (Pillet)s f13 SF 18 r (Non-e)s -2 r (quilibrium)s 18 r (ste)s -1 r (ady)s 18 r (states)s 19 r (of)s 20 r (\014nite)s 19 r (quantum)s 558 2617 p (systems)s 35 r (c)s -1 r (ouple)s -3 r (d)s 34 r (to)s 35 r (thermal)s 35 r (r)s -2 r (eservoirs)s f3 SF 34 r (Commn.Math.Ph)s -1 r (ys.)s f17 SF (226)s f3 SF (,131-)s 558 2684 p (162,\(2002\))s 445 2794 p ([13])s 27 r (O.Lanford)s 19 r (and)s 18 r (D.W.Robinson,)s 19 r (Commn.Math.Ph)s -1 r (ys.)s f17 SF (9)s f3 SF (,327-338,\(1968\))s 445 2905 p ([14])s 27 r (T)s -3 r (aku)s 17 r (Matsui,)s f13 SF 19 r (On)s 19 r (quasi-e)s -2 r (quivalenc)s -2 r (e)s 18 r (of)s 20 r (quasifr)s -2 r (e)s -3 r (e)s 19 r (states)s 20 r (of)s 20 r (the)s 20 r (gauge)s 19 r (in-)s 558 2972 p (variant)s 20 r (CAR)s 20 r (algebr)s -2 r (as.)s f3 SF 18 r (J.Op)s 1 r (erator)s 19 r (Theory)s -4 r (.)s f17 SF 17 r (17)s f3 SF (,281-290\(1987\))s 445 3082 p ([15])s 27 r (Y.Ogata,)s f13 SF (Non-e)s -2 r (quilibrium)s 39 r (Pr)s -2 r (op)s -3 r (erties)s 39 r (in)s 39 r (the)s 39 r (T)s -3 r (r)s -3 r (ansverse)s 39 r (XX)s 39 r (Chain)s f3 SF 558 3149 p (Phy)s -5 r (.Rev.E,)s f17 SF (2)s f3 SF (,016135,)s 18 r (\(2002\))s 445 3259 p ([16])s 27 r (D.Ruelle,)s f13 SF (A)s 17 r (variational)s 17 r (formulation)s 18 r (of)s 17 r (e)s -2 r (quilibrium)s 16 r (statistic)s -2 r (al)s 16 r (me)s -2 r (chanics)s 558 3326 p (and)s 20 r (the)s 20 r (Gibbs)s 20 r (phase)s 20 r (rule.)s f3 SF 18 r (Commn.Math.Phys.)s f17 SF (5)s f3 SF (,324-329,\(1967\))s 1270 3503 p (18)s EP %%Page: 19 19 BP f3 SF 445 349 p ([17])s 27 r (D.)s 27 r (Ruelle,)s f13 SF 29 r (Natur)s -1 r (al)s 26 r (none)s -2 r (quilibrium)s 27 r (states)s 28 r (in)s 27 r (quantum)s 28 r (statistic)s -2 r (al)s 27 r (me-)s 558 415 p (chanics)s 19 r (J.)s 20 r (Stat.)s 19 r (Phys.)s f17 SF 39 r (98)s f3 SF (,)s 18 r (57)s 19 r (\(2000\).)s 445 526 p ([18])s 27 r (D.)s 18 r (Ruelle,)s f13 SF 18 r (Entr)s -1 r (opy)s 18 r (pr)s -2 r (o)s -3 r (duction)s 19 r (in)s 19 r (quantum)s 19 r (spin)s 20 r (systems)s 18 r (Comm.)s 19 r (Math.)s 558 592 p (Phys.)s f17 SF 19 r (224)s f3 SF 21 r (,)s 19 r (3)s 18 r (\(2001\).)s 445 703 p ([19])s 27 r (W.Pusz,)s 18 r (and)s 18 r (S.L.W)s -4 r (orono)s -1 r (wicz,)s f13 SF 17 r (Passive)s 19 r (states)s 19 r (and)s 19 r (KMS)s 19 r (states)s 19 r (for)s 20 r (gen-)s 558 769 p (er)s -1 r (al)s 18 r (quantum)s 20 r (systems)s f3 SF 19 r (Commn.Math.Ph)s -1 r (ys.)s f17 SF (58)s f3 SF (,273-290,\(1978\))s 445 880 p ([20])s 27 r (Shuic)s -2 r (hi)s 35 r (T)s -3 r (asaki,T)s -5 r (aku)s 35 r (Matsui)s f13 SF 37 r (Fluctuation)s 36 r (The)s -2 r (or)s -3 r (em,)s 39 r (None)s -2 r (quilibrium)s 558 946 p (Ste)s -1 r (ady)s 27 r (States)s 28 r (and)s 28 r (MacL)s -1 r (ennan-Zub)s -3 r (ar)s -3 r (ev)s 27 r (Ensembles)s 28 r (of)s f6 SF 29 r (L)s f2 SF 1936 926 p (1)s f13 SF 1961 946 p (-Asymptotic)s 558 1013 p (Ab)s -3 r (elian)s 19 r (C)s f8 SF 796 993 p (\003)s f13 SF 841 1013 p (Dynamic)s -1 r (al)s 18 r (Systems.)s f3 SF 19 r (preprin)s -1 r (t)s 18 r (mp-arh)s 18 r (02-533)s 19 r (\(2002\))s 445 1124 p ([21])s 27 r (D.N.Zubarev,)s f13 SF 19 r (None)s -2 r (quilibrium)s 19 r (Statistic)s -2 r (al)s 19 r (Physics)s f3 SF 18 r (Nauk)s -2 r (a,)s 18 r (317-\(1971\))s 1270 3503 p (19)s EP %%Trailer %%Pages: 19 END %%EOF ---------------0302012204125--