Content-Type: multipart/mixed; boundary="-------------0501140635392" This is a multi-part message in MIME format. ---------------0501140635392 Content-Type: text/plain; name="05-19.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-19.comments" e-mail: sabou@itp.phys.ethz.ch, juerg@itp.phys.ethz.ch ---------------0501140635392 Content-Type: text/plain; name="05-19.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-19.keywords" adiabatic theorem, non-equilibrium statistical mechanics, isothermal processes ---------------0501140635392 Content-Type: application/postscript; name="Iso.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Iso.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: Iso.dvi %%Pages: 14 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMSY10 CMBX10 CMR10 CMTI10 CMMI8 CMBX12 %%+ CMTI12 CMSY7 CMMI12 CMSY8 CMR8 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All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99 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All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF 5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 525003F3DBE5BF07B2E83E66B7F97DDD7CE0EEB75A78BD9227BF359D002B6ADB 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E3948FFB0B4E70F212EC976D65099D84E0D37A7A771C3101D6AD26A0513378F 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82 7DB9DFB4372D3935C286E39EE7AC9FB6A9B5CE4D2FAE1BC0E55AE02BFC464378 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11F1BDB339D9413911FABEFDDA7CA25C7B769360B335953B1186EE2430243F1B 511B6B1F4016A98F4E56E58F7F0F6B945C59AE0FFA3706A4BC08B9905BB78E70 0DDA17F6BC111D17A1883E5F47846B37075745C761F5CB638C7871B2ACD35FDB 004738456B5FEF221F047117E1102EDA7714040C1A1C489F09D31F312438414A 87BB04D6149166DA0C8718D00C3D7C9B8BBF0CB99DDB32C4B1F7F62F2D9D97EA A248CF577B9A47EE40028B51D637AD 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F075EA0A10A15B0ED05D5039DA41B32B16E95 A3CE9725A429B35BAD796912FC328E3A28F96FCADA20A598E247755E7E7FF801 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y(eigen)m(v)m(ector)33 b(\012)903 3054 y Fo(\014)951 3039 y Fm(\()p Fi(t)p Fm(\),)f(then)g(\012)1412 3054 y Fo(\014)1459 3039 y Fm(\()p Fi(t)p Fm(\))g(can)f(b)s(e)h(view)m(ed)h (as)f(an)f Fl(instantane)-5 b(ous)33 b(e)-5 b(quilibrium)328 3159 y Fm(\(or)23 b Fl(r)-5 b(efer)g(enc)g(e)p Fm(\))22 b Fl(state)p Fm(,)j(and)f Fi(\034)1387 3174 y Fg(R)1451 3159 y Fm(\()p Fi(t)p Fm(\))g(is)f(called)h(instan)m(taneous)h (relaxation)f(time)g(of)e Fh(R)s(_)s Fm(\006.)328 3279 y(Let)29 b Fi(\034)40 b Fm(b)s(e)29 b(the)g(time)g(scale)g(o)m(v)m(er)h (whic)m(h)g Fi(L)p Fm(\()p Fi(t)p Fm(\))f(c)m(hanges)h(appreciably)-8 b(.)44 b(Assuming)30 b(that,)328 3400 y(at)k(some)h(time)h Fi(t)955 3415 y Ff(0)994 3400 y Fm(,)f(the)g(state)g(,)g(\011\()p Fi(t)1678 3415 y Ff(0)1718 3400 y Fm(\),)g(of)f Fh(R)23 b(_)h Fm(\006)35 b(is)g(giv)m(en)h(b)m(y)f(\012)2797 3415 y Fo(\014)2845 3400 y Fm(\()p Fi(t)2918 3415 y Ff(0)2957 3400 y Fm(\),)g(it)g(is)g(natural)328 3520 y(to)d(compare)i(the)f (state)g(\011\()p Fi(t)p 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Fi(;)17 b(s)p Fm(\))28 b(=)f Fi(U)1844 954 y Ff(\()p Fo(\034)8 b Ff(\))1943 990 y Fm(\()p Fi(s;)17 b(s)2117 954 y Fg(0)2140 990 y Fm(\))2178 954 y Fg(\003)2217 990 y Fm(.)474 1110 y(\(2\))48 b(With)g(more)g(precise)i(assumptions)f(on)f(the)g(nature)g (of)g(the)g(sp)s(ectrum)h(of)328 1231 y Fh(f)p Fi(L)p Fm(\()p Fi(s)p Fm(\))p Fh(g)p Fm(,)39 b(one)g(can)f(obtain)h (information)f(ab)s(out)f(the)i(sp)s(eed)h(of)d(con)m(v)m(ergence)k(in) e(\(ii\),)328 1351 y(as)33 b Fi(\034)40 b Fh(!)28 b(1)p Fm(;)33 b(see)h([13,14,12].)43 b(A)33 b(p)s(o)m(w)m(erful)h(strategy)g (to)e(obtain)h(suc)m(h)h(information)f(is)328 1471 y(to)j(mak)m(e)h (use)g(of)e(complex)j(sp)s(ectral)e(deformation)g(tec)m(hniques,)k(suc) m(h)e(as)e(dilatation)328 1592 y(or)c(sp)s(ectral-translation)h (analyticit)m(y)-8 b(.)474 1712 y(These)35 b(tec)m(hniques)g(also)e (enable)g(one)g(to)f(pro)m(v)m(e)i(an)474 1833 y(\(3\))43 b Fl(A)-5 b(diab)g(atic)44 b(The)-5 b(or)g(em)43 b(for)h(R)-5 b(esonanc)g(es)p Fm(,)43 b([17].)74 b(This)44 b(result)g(resem)m(bles)h (the)328 1953 y(adiabatic)37 b(theorem)h(describ)s(ed)h(ab)s(o)m(v)m (e,)g(but)e(eigenstates)i(of)d Fi(L)p Fm(\()p Fi(s)p Fm(\))i(are)f(replaced)h(b)m(y)328 2073 y(resonance)50 b(states,)k(and)49 b(one)g(m)m(ust)h(require)g(the)f(adiabatic)g(time)g (scale)h Fi(\034)60 b Fm(to)49 b(b)s(e)328 2194 y(small)32 b(as)g(compared)g(to)f(the)h(life)g(time,)h Fi(\034)1879 2209 y Fo(r)r(es)1982 2194 y Fm(\()p Fi(s)p Fm(\),)f(of)f(a)g (resonance)i(of)e Fi(L)p Fm(\()p Fi(s)p Fm(\),)h(uniformly)328 2314 y(in)39 b Fi(s)f Fh(2)g Fi(I)8 b Fm(.)62 b(\(F)-8 b(or)38 b(shap)s(e)h(resonances,)j(the)d(tec)m(hniques)j(in)d([18])f (are)h(useful.)63 b(Precise)328 2434 y(statemen)m(ts)24 b(and)f(pro)s(ofs)e(can)i(b)s(e)f(found)h(in)f([17].\))40 b(Similar)23 b(ideas)g(lead)f(to)g(an)h(adiabatic)328 2555 y(theorem)33 b(in)g(non-equilibrium)h(statistical)g(mec)m(hanics,) h([22].)328 2888 y Fn(3)161 b(The)53 b(\\Isothermal)h(Theorem")328 3107 y Fm(In)26 b(this)h(section,)i(w)m(e)e(turn)f(to)g(the)g(study)i (of)d(isothermal)i(pro)s(cesses)h(of)e(\\small")g(driv)m(en)328 3227 y(quan)m(tum)36 b(systems,)i(\006,)e(in)f(diathermal)h(con)m(tact) f(with)h(a)f(heat)g(bath,)g Fh(R)p Fm(,)h(at)f(a)g(\014xed)328 3347 y(temp)s(erature)e(\()p Fi(k)s(\014)6 b Fm(\))1074 3311 y Fg(\000)p Ff(1)1168 3347 y Fm(.)44 b(Our)32 b(notations)h(are)g (as)f(in)h(Sect.1;)g(see,)h(eqs.\(1\),)g(\(2\),)e(\(3\).)474 3468 y(Let)39 b Fi(L)721 3483 y Fo(\034)765 3468 y Fm(\()p Fi(t)p Fm(\))e(:=)h Fi(L)p Fm(\()1175 3429 y Fo(t)p 1168 3445 39 4 v 1168 3502 a(\034)1218 3468 y Fm(\))g(denote)h(the)g (Liouvillian)h(of)e(the)h(coupled)g(system)i Fh(R)27 b(_)f Fm(\006,)328 3588 y(where)38 b Fh(f)p Fi(L)p Fm(\()p Fi(s)p Fm(\))p Fh(g)902 3603 y Fo(s)p Fg(2)p Fo(I)1058 3588 y Fm(is)f(as)g(in)h(eqs.\(2\))f(and)g(\(3\))g(of)f(Sect.1)h(and)g (satis\014es)i(assumptions)328 3709 y(\(A1\))32 b(and)h(\(A2\))f(of)g (Sect.2.)44 b(The)34 b(in)m(terv)-5 b(al)1504 3970 y Fi(I)1547 3985 y Fo(\034)1618 3970 y Fm(=)27 b Fh(f)p Fi(t)h Fh(j)1908 3903 y Fi(t)p 1899 3947 54 4 v 1899 4038 a(\034)1990 3970 y Fh(2)g Fi(I)36 b Fh(\032)28 b Fd(R)p Fh(g)328 4215 y Fm(is)33 b(the)g(time)g(in)m(terv)-5 b(al)33 b(during)g(whic)m(h)i(an)d(isothermal)h(pro)s(cess)h(of)e Fh(R)23 b(_)f Fm(\006)33 b(is)h(studied.)474 4336 y(W)-8 b(e)32 b(assume)i(that)d(\006)h(is)h(driv)m(en)g(\\slo)m(wly",)g(i.e.,) g(that)e Fi(\034)44 b Fm(is)32 b(large)g(as)f(compared)i(to)328 4456 y(the)g(relaxation)g(time)g Fi(\034)1218 4471 y Fg(R)1311 4456 y Fm(=)27 b(max)1596 4471 y Fo(s)p Fg(2)p Fo(I)1732 4456 y Fi(\034)1774 4471 y Fg(R)1839 4456 y Fm(\()p Fi(s)p Fm(\))32 b(of)g Fh(R)23 b(_)f Fm(\006.)474 4577 y(Assumption)34 b(\(A3\))d(of)g(Sect.2)i(is)f(supplemen)m(ted)j (with)d(the)g(follo)m(wing)g(more)h(sp)s(e-)328 4697 y(ci\014c)g(assumption.)474 4817 y(\(A4\))d(F)-8 b(or)29 b(all)h Fi(s)e Fh(2)g Fi(I)35 b Fh(\021)28 b Fm([)p Fi(s)1431 4832 y Ff(0)1471 4817 y Fi(;)17 b(s)1561 4832 y Ff(1)1600 4817 y Fm(],)31 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Fm(where)24 b Fi(a)e Fm(is)h(an)g(arbitrary)f(b)s(ounded)h(op)s(erator)f(on)g Fh(H)29 b Fm(=)f Fh(H)2489 595 y Fg(R_)p Ff(\006)2651 631 y Fm(.)40 b(Then)24 b(the)f(isothermal)328 751 y(theorem)33 b(sa)m(ys)h(that)1439 872 y Fi(\032)1489 887 y Fo(t)1519 872 y Fm(\()p Fi(a)p Fm(\))27 b(=)h Fi(!)1842 825 y Fo(\014)1838 894 y(t)1888 872 y Fm(\()p Fi(a)p Fm(\))23 b(+)f Fi(\017)2175 821 y Ff(\()p Fo(\034)8 b Ff(\))2175 894 y Fo(t)2273 872 y Fm(\()p Fi(a)p Fm(\))28 b Fi(;)937 b Fm(\(16\))328 1046 y(where)1584 1223 y(lim)1561 1282 y Fo(\034)8 b Fg(!1)1768 1155 y Fh(j)p Fi(\017)1835 1104 y Ff(\()p Fo(\034)g Ff(\))1835 1178 y Fo(t)1933 1155 y Fm(\()p Fi(a)p Fm(\))p Fh(j)p 1768 1200 320 4 v 1847 1291 a(jj)p Fi(a)p Fh(jj)2125 1223 y Fm(=)28 b(0)f Fi(;)1060 b Fm(\(17\))328 1447 y(for)32 b(all)g(times)i Fi(t)28 b Fh(2)g Fi(I)1073 1462 y Fo(\034)1116 1447 y Fm(.)474 1568 y(\(3\))j(If)g(the)g(complex)i (sp)s(ectral)f(deformation)f(tec)m(hniques)j(of)d([2,3])g(are)g (applicable)328 1688 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b(are)f(giv)m(en)i(b)m(y)1415 3536 y Fa(P)1477 3489 y Fo(\014)1477 3563 y Fg(R)1569 3536 y Fm(=)28 b(\()p Fi(Z)1785 3489 y Fo(\014)1778 3563 y Fg(R)1842 3536 y Fm(\))1880 3495 y Fg(\000)p Ff(1)1974 3536 y Fi(e)2019 3495 y Fg(\000)p Fo(\014)s(H)2180 3471 y Fc(R)2269 3536 y Fi(;)1096 b Fm(\(26\))1570 3695 y Fi(Z)1644 3648 y Fo(\014)1637 3722 y Fg(R)1729 3695 y Fm(=)28 b Fi(tr)s Fm(\()p Fi(e)1998 3654 y Fg(\000)p Fo(\014)s(H)2159 3630 y Fc(R)2220 3695 y Fm(\))g Fi(;)1079 b Fm(\(27\))328 3915 y(resp)s(ectiv)m(ely)-8 b(.)474 4035 y(Next,)27 b(w)m(e)f(in)m(tro)s(duce)f Fl(thermo)-5 b(dynamic)26 b(p)-5 b(otentials)24 b Fm(for)g(the)h(small)g(system)h (\006:)40 b(The)328 4156 y Fl(internal)34 b(ener)-5 b(gy)33 b Fm(of)f(\006)h(in)f(the)h(\\true")g(state,)g Fi(\032)2116 4171 y Fo(t)2146 4156 y Fm(,)g(of)f Fh(R)22 b(_)h Fm(\006)33 b(at)f(time)h Fi(t)g Fm(is)g(de\014ned)h(b)m(y)1541 4376 y Fi(U)1617 4334 y Ff(\006)1673 4376 y Fm(\()p Fi(t)p Fm(\))28 b(:=)f Fi(\032)1992 4391 y Fo(t)2022 4376 y 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Fm(carried)h(out)g(b)m(y)h Fh(R)22 b(_)h Fm(\006:)44 b(the)34 b Fl(he)-5 b(at)35 b(\015ux)e Fm(in)m(to)g(\006)g(and)g(the)g Fl(work)328 2091 y(r)-5 b(ate)p Fm(,)28 b(or)d Fl(p)-5 b(ower)p Fm(,)27 b(of)f(\006.)41 b(Let)27 b Fi(\016)j Fm(denote)d(the)f(so)g(called)h(\\imp)s(erfect)g(di\013eren)m(tial".)43 b(Then)1200 2300 y Fi(\016)t(Q)1324 2264 y Ff(\006)p 1200 2344 180 4 v 1247 2436 a Fi(dt)1389 2367 y Fm(\()p Fi(t)p Fm(\))28 b(:=)g Fi(T)14 b(D)19 b Fm(lim)1867 2429 y Fg(R)1982 2367 y Fh(\000)2087 2300 y Fi(d)p 2069 2344 86 4 v 2069 2436 a(dt)2165 2367 y(tr)s Fm(\()p Fa(P)p Fm(\()p Fi(t)p Fm(\))p Fi(H)2547 2326 y Fg(R)2611 2367 y Fm(\))28 b Fi(;)688 b Fm(\(32\))328 2616 y(and)1492 2706 y Fi(\016)t(A)1612 2670 y Ff(\006)p 1492 2751 176 4 v 1537 2842 a Fi(dt)1677 2774 y Fm(\()p Fi(t)p Fm(\))28 b(:=)f Fi(\032)1996 2789 y Fo(t)2026 2774 y Fm(\()2100 2748 y(_)2064 2774 y Fi(H)2153 2733 y Ff(\006)2208 2774 y Fm(\()p Fi(t)p Fm(\)\))h(;)980 b(\(33\))328 2979 y(see)34 b([12,1,8])e(for)g(details.)474 3099 y(W)-8 b(e)36 b(are)f(no)m(w)h (prepared)g(to)f(summarize)i(our)f(main)f(results)i(on)e(isothermal)h (pro-)328 3220 y(cesses.)474 3340 y(\(1\))g(F)-8 b(rom)36 b(de\014nitions)i(\(28\),)f(\(32\))e(and)i(\(33\))f(and)g(the)h (Liouville)g(equation)g(\(21\))328 3460 y(it)32 b(follo)m(ws)i(that) 1392 3593 y(_)1364 3618 y Fi(U)1440 3577 y Ff(\006)1496 3618 y Fm(\()p Fi(t)p Fm(\))28 b(=)1748 3550 y Fi(\016)t(Q)1872 3514 y Ff(\006)p 1748 3595 180 4 v 1795 3686 a Fi(dt)1937 3618 y Fm(\()p Fi(t)p Fm(\))23 b(+)2179 3550 y Fi(\016)t(A)2299 3514 y Ff(\006)p 2179 3595 176 4 v 2223 3686 a Fi(dt)2364 3618 y Fm(\()p Fi(t)p Fm(\))28 b Fi(;)862 b Fm(\(34\))328 3823 y(whic)m(h)38 b(is)e(the)h Fl(\014rst)h(law)g(of)f(thermo)-5 b(dynamics)p Fm(;)37 b(\(hardly)g(more)f(than)g(a)g(de\014nition)h(of) 338 3914 y Fo(\016)r(A)424 3890 y Fb(\006)p 338 3930 135 4 v 374 3987 a Fo(dt)482 3953 y Fm(\).)474 4073 y(\(2\))27 b(Note)h(that,)g(b)m(y)h(the)f(unitarit)m(y)g(of)f(time)h(ev)m(olution) h(and)f(the)f(cyclic)j(in)m(v)-5 b(ariance)328 4194 y(of)32 b(the)h(trace,)1507 4291 y Fi(d)p 1490 4335 86 4 v 1490 4426 a(dt)1586 4358 y(tr)s Fm(\()p Fa(P)p Fm(\()p Fi(t)p Fm(\))p Fi(l)r(n)p Fa(P)p Fm(\()p Fi(t)p Fm(\)\))28 b(=)f(0)h Fi(;)328 4558 y Fm(and)1300 4635 y Fi(d)p 1282 4680 V 1282 4771 a(dt)1378 4703 y(tr)s Fm(\()p Fa(P)p Fm(\()p Fi(t)p Fm(\))p Fi(l)r(nZ)1834 4655 y Fo(\014)1827 4730 y Fg(R)1891 4703 y Fm(\))g(=)2088 4635 y Fi(d)p 2071 4680 V 2071 4771 a(dt)2166 4703 y(l)r(nZ)2329 4655 y Fo(\014)2322 4730 y Fg(R)2415 4703 y Fm(=)f(0)h Fi(:)1898 5214 y Fm(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 328 631 a Fm(T)-8 b(ogether)33 b(with)g(de\014nitions)h(\(26\),)e(\(29\))g(and)h(\(32\),)f(this)h (implies)h(that)1565 876 y(_)1537 902 y Fi(S)1603 860 y Ff(\006)1658 902 y Fm(\()p Fi(t)p Fm(\))28 b(=)1922 834 y(1)p 1911 879 71 4 v 1911 970 a Fi(T)2001 834 y(\016)t(Q)2125 798 y Ff(\006)p 2001 879 180 4 v 2048 970 a Fi(dt)2190 902 y Fm(\()p Fi(t)p Fm(\))g Fi(;)1036 b Fm(\(35\))328 1146 y(for)32 b Fl(arbitr)-5 b(ary)33 b Fm(isothermal)g(pro)s(cesses)i (at)d(temp)s(erature)i Fi(T)41 b Fm(=)28 b(\()p Fi(k)s(\014)6 b Fm(\))2849 1109 y Fg(\000)p Ff(1)2942 1146 y Fm(.)474 1266 y(\(3\))30 b(Next,)h(w)m(e)f(consider)i(an)d(isothermal)i(pro)s (cess)g(of)e Fh(R)16 b(_)g Fm(\006)31 b(during)f(a)g(\014nite)g(time) 328 1386 y(in)m(terv)-5 b(al)28 b Fi(I)718 1401 y Fo(\034)789 1386 y Fm(=)g([)p Fi(\034)11 b(s)1019 1401 y Ff(0)1059 1386 y Fi(;)17 b(\034)11 b(s)1202 1401 y Ff(1)1241 1386 y Fm(],)29 b(with)g Fi(s)1588 1401 y Ff(0)1655 1386 y Fm(and)f Fi(s)1886 1401 y Ff(1)1953 1386 y Fm(\014xed.)43 b(The)29 b(initial)f(state)g Fi(\032)2982 1401 y Fo(\034)8 b(s)3054 1410 y Fb(0)3120 1386 y Fm(of)27 b Fh(R)12 b(_)g Fm(\006)30 b(is)328 1507 y(assumed)36 b(to)e(b)s(e)g(an)h(equilibrium)h (state)f Fi(!)1939 1471 y Fo(\014)1935 1531 y(\034)8 b(s)2007 1540 y Fb(0)2079 1507 y Fm(of)34 b(the)h(Liouvillian)g Fi(L)2916 1522 y Fo(\034)2959 1507 y Fm(\()p Fi(\034)11 b(s)3096 1522 y Ff(0)3136 1507 y Fm(\))31 b(=)f Fi(L)p Fm(\()p Fi(s)3461 1522 y Ff(0)3501 1507 y Fm(\).)328 1627 y(W)-8 b(e)33 b(are)g(in)m(terested)i(in)f(the)f(prop)s(erties)h (of)e(suc)m(h)j(a)e(pro)s(cess)h(when)g Fi(\034)44 b Fm(b)s(ecomes)35 b(large,)328 1748 y(i.e.,)e(when)h(the)f(pro)s(cess)h (is)f Fl(quasi-static)p Fm(.)474 1986 y Fl(R)-5 b(esult.)43 b Fm(Quasi-static)30 b(isothermal)h(pro)s(cesses)g(are)f Fl(r)-5 b(eversible)29 b Fm(\(in)g(the)h(sense)i(that)328 2106 y(all)c(in)m(termediate)j(states)e Fi(\032)1345 2121 y Fo(t)1404 2106 y Fm(of)f Fh(R)14 b(_)g Fm(\006,)30 b Fi(t)e Fh(2)g Fi(I)2016 2121 y Fo(\034)2059 2106 y Fm(,)i(con)m(v)m(erge)g(in)f(norm)f(to)g Fl(instantane)-5 b(ous)328 2227 y(e)g(quilibrium)34 b(states)f Fi(!)1169 2180 y Fo(\014)1165 2249 y(t)1215 2227 y Fm(,)g(as)g Fi(\034)39 b Fh(!)27 b(1)p Fm(\).)474 2347 y(This)41 b(result)g(is)g(an)f(immediate)h(consequence)i(of)d(the)g(isothermal)h (theorem.)67 b(It)328 2468 y(means)32 b(that,)f(for)g(all)g(practical)h (purp)s(oses,)h(an)e(isothermal)h(pro)s(cess)g(with)g(time)g(scale)328 2588 y Fi(\034)44 b Fm(is)33 b(rev)m(ersible)i(if)e Fi(\034)39 b Fh(\035)27 b Fi(\034)1286 2603 y Fg(R)1378 2588 y Fm(=)h(max)1664 2603 y Fo(s)p Fg(2)p Fo(I)1800 2588 y Fi(\034)1842 2603 y Fg(R)1907 2588 y Fm(\()p Fi(s)p Fm(\).)474 2708 y(\(4\))36 b(F)-8 b(or)36 b(rev)m(ersible)j(isothermal)e(pro)s(cesses,)i(the)e (usual)g Fl(e)-5 b(quilibrium)38 b(de\014nitions)328 2829 y Fm(of)32 b(in)m(ternal)h(energy)h(and)f(en)m(trop)m(y)h(of)e (the)h(small)g(system)i(\006)e(can)f(b)s(e)h(used:)1477 3038 y Fi(U)1553 2996 y Ff(\006)1543 3062 y Fo(r)r(ev)1651 3038 y Fm(\()p Fi(t)p Fm(\))27 b(:=)h Fi(!)1985 2990 y Fo(\014)1981 3060 y(t)2031 3038 y Fm(\()p Fi(H)2158 2996 y Ff(\006)2213 3038 y Fm(\()p Fi(t)p Fm(\)\))g Fi(;)975 b Fm(\(36\))378 3291 y Fi(S)444 3250 y Ff(\006)438 3315 y Fo(r)r(ev)545 3291 y Fm(\()p Fi(t)p Fm(\))28 b(:=)g Fh(\000)p Fi(k)j(T)14 b(D)19 b Fm(lim)1182 3353 y Fg(R)1297 3291 y Fi(tr)s Fm(\()p Fa(P)1479 3250 y Fo(\014)1526 3291 y Fm(\()p Fi(t)p Fm(\)[)p Fi(l)r(n)p Fa(P)1815 3250 y Fo(\014)1863 3291 y Fm(\()p Fi(t)p Fm(\))13 b Fh(\000)g Fi(l)r(n)p Fa(P)2228 3250 y Fg(R)2294 3291 y Fm(]\))27 b(=)2511 3223 y(1)p 2500 3268 71 4 v 2500 3359 a Fi(T)2580 3291 y Fm(\()p Fi(U)2694 3250 y Ff(\006)2684 3315 y Fo(r)r(ev)2792 3291 y Fm(\()p Fi(t)p Fm(\))13 b Fh(\000)g Fi(F)3083 3250 y Ff(\006)3139 3291 y Fm(\()p Fi(t)p Fm(\)\))27 b Fi(;)50 b Fm(\(37\))328 3502 y(where)25 b(the)f(free)h(energy)g Fi(F)1319 3466 y Ff(\006)1373 3502 y Fm(\()p Fi(t)p Fm(\))f(has)g(b)s (een)h(de\014ned)g(in)f(\(31\),)i(and)e(the)g(second)h(equation)328 3622 y(in)34 b(\(37\))e(follo)m(ws)j(from)e(\(22\),)g(\(26\),)g(\(31\)) g(and)g(\(36\).)46 b(Eqs.\(37\))34 b(and)g(\(31\))f(then)h(imply)328 3743 y(that)1103 3862 y(_)1075 3887 y Fi(S)1141 3846 y Ff(\006)1135 3912 y Fo(r)r(ev)1243 3887 y Fm(\()p Fi(t)p Fm(\))28 b(=)1506 3820 y(1)p 1495 3865 V 1495 3956 a Fi(T)1576 3887 y Fm(\()1641 3820 y Fi(d)p 1624 3865 86 4 v 1624 3956 a(dt)1720 3887 y(!)1785 3840 y Fo(\014)1781 3910 y(t)1831 3887 y Fm(\()p Fi(H)1958 3846 y Ff(\006)2013 3887 y Fm(\()p Fi(t)p Fm(\)\))22 b Fh(\000)g Fi(!)2348 3840 y Fo(\014)2344 3910 y(t)2395 3887 y Fm(\()2469 3862 y(_)2433 3887 y Fi(H)2522 3846 y Ff(\006)2577 3887 y Fm(\()p Fi(t)p Fm(\)\)\))27 b Fi(:)328 4088 y Fm(Recalling)33 b(\(34\))f(and)h(\(35\),)f(and)g(applying)i(the)f(isothermal)g (theorem,)h(w)m(e)f(\014nd)g(that)1651 4272 y(_)1624 4297 y Fi(S)1690 4256 y Ff(\006)1745 4297 y Fm(\()p Fi(t)p Fm(\))28 b Fh(!)2038 4272 y Fm(_)2011 4297 y Fi(S)2077 4256 y Ff(\006)2071 4321 y Fo(r)r(ev)2178 4297 y Fm(\()p Fi(t)p Fm(\))g Fi(;)1048 b Fm(\(38\))1560 4448 y Fi(\016)t(A)1680 4412 y Ff(\006)p 1560 4492 176 4 v 1604 4583 a Fi(dt)1745 4515 y Fm(\()p Fi(t)p Fm(\))28 b Fh(!)2044 4490 y Fm(_)2011 4515 y Fi(F)2088 4474 y Ff(\006)2143 4515 y Fm(\()p Fi(t)p Fm(\))f Fi(;)1084 b Fm(\(39\))328 4724 y(as)33 b Fi(\034)39 b Fh(!)27 b(1)p Fm(.)474 4844 y(\(5\))42 b(W)-8 b(e)42 b(conclude)h(this)g(o)m(v)m(erview)h(b)m(y)f(considering)g(a)f (quasi-static)h(isothermal)328 4965 y(pro)s(cess)24 b(of)f Fh(R)s(_)s Fm(\006)h(with)f Fi(H)1311 4929 y Ff(\006)1366 4965 y Fm(\()p Fi(s)p Fm(\))k Fh(!)h Fi(H)1732 4929 y Ff(\006)1724 4989 y(0)1786 4965 y Fi(;)45 b(g)t Fm(\()p Fi(s)p Fm(\))27 b Fh(!)g Fm(0,)e(as)e Fi(s)28 b Fh(\045)f Fi(s)2643 4980 y Ff(1)2682 4965 y Fm(,)e(i.e.,)h(the)d(in)m(teractions) 1898 5214 y(11)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 328 631 a Fm(b)s(et)m(w)m(een)49 b Fh(R)f Fm(and)f(\006)h(are)f(switc)m(hed)i(o\013)e(at)g(the)g(end)h (of)f(the)h(pro)s(cess.)88 b(Then)48 b(the)328 751 y(isothermal)33 b(theorem)h(implies)g(that)1440 971 y(lim)1418 1031 y Fo(\034)8 b Fg(!1)1632 971 y Fm(lim)1614 1034 y Fo(s)p Fg(\045)p Fo(s)1751 1043 y Fb(1)1801 971 y Fi(\032)1851 986 y Fo(\034)g(s)1955 971 y Fm(=)28 b Fi(!)2124 924 y Fo(\014)2120 998 y Fg(R)2206 971 y Fh(\012)23 b Fi(!)2371 924 y Fo(\014)2367 998 y Ff(\006)2449 971 y Fi(;)916 b Fm(\(40\))328 1259 y(where)34 b Fi(!)675 1211 y Fo(\014)671 1286 y Fg(R)735 1259 y Fm(\()p Fh(\001)p Fm(\))27 b(=)h(\()p Fi(Z)1082 1211 y Fo(\014)1075 1286 y Fg(R)1139 1259 y Fm(\))1177 1222 y Fg(\000)p Ff(1)1271 1259 y Fi(tr)s Fm(\()p Fi(e)1436 1222 y Fg(\000)p Fo(\014)s(H)1597 1199 y Fc(R)1658 1259 y Fh(\001)p Fm(\),)k(see)i(\(26\),)e(and)1404 1492 y Fi(!)1469 1445 y Fo(\014)1465 1519 y Ff(\006)1520 1492 y Fm(\()p Fh(\001)p Fm(\))27 b(=)g(\()p Fi(Z)1866 1445 y Fo(\014)1859 1519 y Ff(\006)1914 1492 y Fm(\))1952 1451 y Fg(\000)p Ff(1)2047 1492 y Fi(tr)s Fm(\()p Fi(e)2212 1451 y Fg(\000)p Fo(\014)s(H)2373 1428 y Fb(\006)2368 1472 y(0)2424 1492 y Fh(\001)p Fm(\))902 b(\(41\))328 1712 y(is)39 b(the)g(Gibbs)g(state)g(of)f(the)g(small)h(system)i(\006)e (at)f(the)h(temp)s(erature)g(\()p Fi(k)s(\014)6 b Fm(\))3181 1676 y Fg(\000)p Ff(1)3313 1712 y Fm(of)38 b(the)328 1832 y(heat)33 b(bath,)g Fl(indep)-5 b(endently)31 b Fm(of)h(the)h(prop)s(erties)h(of)e(the)h(diathermal)h(con)m(tact)f (\(i.e.,)g(of)328 1953 y(the)g(in)m(teraction)g(Hamiltonian)g Fi(W)14 b Fm(\),)32 b(assuming)i(that)f(\(A1\)-\(A4\))e(hold)i(for)f Fi(s)c(<)f(s)3435 1968 y Ff(1)3475 1953 y Fm(.)474 2073 y(This)40 b(result)f(and)f(the)g(prop)s(ert)m(y)h(of)f(return)g(to)g (equilibrium)i(for)e(the)g(heat)h(bath)328 2194 y Fh(R)33 b Fm(yield,)h(in)f(essence,)i(the)e(0)1403 2157 y Fo(th)1505 2194 y Fm(la)m(w)g(of)g(thermo)s(dynamics.)474 2314 y(Carnot)45 b(pro)s(cesses)i(and)e(the)h(2)1683 2278 y Fo(nd)1811 2314 y Fm(la)m(w)f(of)g(thermo)s(dynamics)i(are)e(discussed)j(in)328 2434 y([1];)35 b(\(see)h(also)e([10,20,21]\).)49 b(An)34 b(imp)s(ortan)m(t)h(v)-5 b(arian)m(t)34 b(of)g(the)h(adiabatic)g (theorem)g(for)328 2555 y(non-equilibrium)g(stationary)f(states)h(will) g(app)s(ear)e(in)h([22].)47 b(The)35 b(analysis)g(in)f([22])f(is)328 2675 y(based)g(on)g(some)g(basic)h(tec)m(hniques)h(dev)m(elop)s(ed)g (in)e([23].)328 3008 y Fn(References)328 3227 y Fm([1])49 b(W.K.)e(Ab)s(ou-Salem)g(and)g(J.)g(F)-8 b(r\177)-49 b(ohlic)m(h,)51 b Fl(Status)e(of)e(the)i(fundamental)e(laws)g(of)431 3347 y(thermo)-5 b(dynamics)p Fm(,)31 b(in)i(preparation)328 3551 y([2])49 b(V.)38 b(Jaksi)m(\023)-46 b(c)40 b(and)e(C.-A.)h (Pillet,)i Fl(On)f(a)g(mo)-5 b(del)39 b(of)h(quantum)g(friction)g(II:)f (F)-7 b(ermi's)431 3671 y(golden)46 b(rule)i(and)f(dynamics)g(at)g(p)-5 b(ositive)47 b(temp)-5 b(er)g(atur)g(e)p Fm(,)50 b(Comm.)d(Math.)g(Ph)m (ys.)431 3792 y Fe(176)p Fm(,)33 b(no.3,)f(619-644)f(\(1996\))328 3995 y([3])49 b(V.)35 b(Jaksi)m(\023)-46 b(c)37 b(and)f(C.-A.)g (Pillet,)h Fl(On)h(a)f(mo)-5 b(del)37 b(of)g(quantum)h(friction)f(III:) f(Er)-5 b(go)g(dic)431 4115 y(pr)g(op)g(erties)38 b(of)h(the)f(spin-b) -5 b(oson)38 b(system)p Fm(,)g(Comm.)f(Math.)g(Ph)m(ys.)i Fe(178)p Fm(,)f(no.3,)g(627-)431 4236 y(651)32 b(\(1996\))328 4439 y([4])49 b(V.)25 b(Bac)m(h,)j(J.)d(F)-8 b(r\177)-49 b(ohlic)m(h)26 b(and)g(I.M.)g(Sigal,)h Fl(R)-5 b(eturn)29 b(to)f(e)-5 b(quilibrium)p Fm(,)27 b(J.)e(Math.)h(Ph)m(ys.)431 4559 y Fe(41)p Fm(,)33 b(no.6,)f(3985-4060)e(\(2000\))328 4763 y([5])49 b(M.)37 b(Merkli,)i Fl(Positive)f(c)-5 b(ommutators)38 b(in)g(non-e)-5 b(quilibrium)37 b(quantum)i(statistic) -5 b(al)431 4883 y(me)g(chanics)p Fm(,)31 b(Comm.)i(Math.)g(Ph)m(ys.)i Fe(223)p Fm(,)d(no.2,)h(327-362)e(\(2001\))1898 5214 y(12)p eop end %%Page: 13 13 TeXDict begin 13 12 bop 328 631 a Fm([6])49 b(J.)c(F)-8 b(r\177)-49 b(ohlic)m(h)46 b(and)f(M.)h(Merkli,)k Fl(A)n(nother)c(r)-5 b(eturn)47 b(of)g(\\r)-5 b(eturn)47 b(to)f(e)-5 b(quilibrium")p Fm(,)431 751 y(Comm.)33 b(Math.)g(Ph)m(ys.)i Fe(251)p Fm(,)d(no.2,)h(235-262)e(\(2004\))328 955 y([7])49 b(D.W.)32 b(Robinson,)h Fl(R)-5 b(eturn)35 b(to)g(e)-5 b(quilibrium)p Fm(,)32 b(Comm.)i(Math.)f(Ph)m(ys.)h Fe(31)p Fm(,)f(171-189)431 1075 y(\(1973\))328 1279 y([8])49 b(J.)28 b(F)-8 b(r\177)-49 b(ohlic)m(h,)29 b(M.)g(Merkli,)h(D.)e(Ueltsc)m(hi,)j(and)d(S.)h(Sc)m(h) m(w)m(arz,)i Fl(Statistic)-5 b(al)30 b(me)-5 b(chanics)431 1399 y(of)41 b(thermo)-5 b(dynamic)40 b(pr)-5 b(o)g(c)g(esses)p Fm(,)41 b(in)f Fl(A)h(gar)-5 b(den)41 b(of)g(quanta)p Fm(,)h(345-363,)d(W)-8 b(orld)40 b(Sci.)431 1519 y(Publishing,)34 b(Riv)m(er)g(Edge,)f(NJ)g(\(2003\))328 1723 y([9])49 b(R.)43 b(Haag,)j(N.M.)f(Hugenholtz)f(and)g(M.)g(Winnink,)49 b Fl(On)44 b(e)-5 b(quilibrium)45 b(states)g(in)431 1843 y(quantum)35 b(statistic)-5 b(al)35 b(me)-5 b(chanics)p Fm(,)31 b(Comm.)i(Math.)g(Ph)m(ys.)i Fe(5)p Fm(,)d(215-236)f(\(1967\)) 328 2046 y([10])48 b(O.)35 b(Bratelli)f(and)h(D.W.)f(Robinson,)h Fl(Op)-5 b(er)g(ator)36 b(algebr)-5 b(as)35 b(and)h(quantum)h(statis-) 431 2167 y(tic)-5 b(al)45 b(me)-5 b(chanics)43 b(I,II)p Fm(,)f(T)-8 b(exts)46 b(and)d(Monographs)i(in)e(Ph)m(ysics,)50 b(Springer-V)-8 b(erlag)431 2287 y(\(1987\))328 2491 y([11])48 b(W.K.)33 b(Ab)s(ou-Salem,)g Fl(PhD)h(thesis)f Fm(\(2005\))328 2694 y([12])48 b(W.K.)33 b(Ab)s(ou-Salem)g(and)g(J.)f (F)-8 b(r\177)-49 b(ohlic)m(h,)33 b(in)g(preparation)328 2897 y([13])48 b(J.E.)40 b(Avron)f(and)h(A.)f(Elgart,)h Fl(A)-5 b(diab)g(atic)41 b(the)-5 b(or)g(em)40 b(without)h(a)f(gap)h(c) -5 b(ondition)p Fm(,)431 3018 y(Comm.)33 b(Math.)g(Ph)m(ys.)i Fe(203)p Fm(,)d(no.2,)h(445-463)e(\(1999\))328 3221 y([14])48 b(S.)33 b(T)-8 b(eufel,)34 b Fl(A)h(note)g(on)g(the)g(adiab)-5 b(atic)34 b(the)-5 b(or)g(em)p Fm(,)32 b(Lett.)h(Math.)g(Ph)m(ys.)h Fe(58)p Fm(,)f(no.3,)431 3342 y(261-266)e(\(2002\))328 3545 y([15])48 b(M.)27 b(Reed)g(and)f(B.)g(Simon,)i Fl(Metho)-5 b(ds)29 b(of)g(mo)-5 b(dern)28 b(mathematic)-5 b(al)28 b(physics)p Fm(,)f(v)m(ol.I)s(I,)431 3665 y(Academic)34 b(Press,)g(NY)f(\(1975\))328 3869 y([16])48 b(K.)33 b(Y)-8 b(osida,)33 b Fl(F)-7 b(unctional)33 b(analysis)p Fm(,)f(6th)h(ed.,)g (Springer-V)-8 b(erlag)33 b(\(1998\))328 4072 y([17])48 b(W.K.)30 b(Ab)s(ou-Salem)f(and)g(J.)g(F)-8 b(r\177)-49 b(ohlic)m(h,)30 b Fl(A)-5 b(diab)g(atic)32 b(the)-5 b(or)g(em)31 b(for)g(r)-5 b(esonanc)g(es)p Fm(,)29 b(in)431 4193 y(preparation)328 4396 y([18])48 b(J.)30 b(F)-8 b(r\177)-49 b(ohlic)m(h)29 b(and)g(P)-8 b(.)30 b(Pfeifer,)g Fl(Gener)-5 b(alize)g(d)31 b(time-ener)-5 b(gy)31 b(unc)-5 b(ertainty)32 b(r)-5 b(elations)431 4516 y(and)27 b(b)-5 b(ounds)26 b(on)h(lifetimes)g(of)g (r)-5 b(esonanc)g(es)p Fm(,)24 b(Rev.)i(Mo)s(d.)e(Ph)m(ys.)i Fe(67)p Fm(,)g(759-779)d(\(1995\))328 4720 y([19])48 b(D.)22 b(Ruelle,)j Fl(Statistic)-5 b(al)25 b(me)-5 b(chanics:)38 b(rigor)-5 b(ous)25 b(r)-5 b(esults)p Fm(,)24 b(Imp)s(erial)e(College)h (Press,)431 4840 y(London)33 b(\(1999\))1898 5214 y(13)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 328 631 a Fm([20])48 b(D.)34 b(Ruelle,)i Fl(Entr)-5 b(opy)36 b(pr)-5 b(o)g(duction)36 b(in)g(quantum)g(spin)g(systems)p Fm(,)e(Comm.)h(Math.)431 751 y(Ph)m(ys.)f Fe(224)p Fm(,)f(no.1,)g(3-16)e(\(2001\))328 955 y([21])48 b(J.)40 b(F)-8 b(r\177)-49 b(ohlic)m(h,)41 b(M.)e(Merkli)i(and)e(D.)f(Ueltsc)m(hi,)43 b Fl(Dissip)-5 b(ative)40 b(tr)-5 b(ansp)g(ort:)56 b(thermal)431 1075 y(c)-5 b(ontacts)41 b(and)h(tunnel)5 b(ling)41 b(junctions)p Fm(,)h(Ann.)e(Henri)h(P)m(oincar)m(\023)-46 b(e)42 b Fe(4)p Fm(,)g(no.5,)g(897-945)431 1196 y(\(2003\))328 1399 y([22])48 b(W.K.)54 b(Ab)s(ou-Salem,)59 b Fl(A)n(n)54 b(adiab)-5 b(atic)53 b(the)-5 b(or)g(em)54 b(for)g(non-e)-5 b(quilibrium)53 b(ste)-5 b(ady)431 1519 y(states)p Fm(,)33 b(in)f(preparation)328 1723 y([23])48 b(V.)32 b(Jaksi)m(\023)-46 b(c)32 b(and)f(C.-A.)g(Pillet,)h Fl(Non-e)-5 b(quilibrium)33 b(ste)-5 b(ady)34 b(states)f(of)g(\014nite)g(quan-)431 1843 y(tum)e(systems)f(c)-5 b(ouple)g(d)30 b(to)h(thermal)f(r)-5 b(eservoirs)p Fm(,)28 b(Comm.)h(Math.)f(Ph)m(ys.)i Fe(226)p Fm(,)f(no.1,)431 1963 y(131-162)i(\(2002\))1898 5214 y(14)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0501140635392--