Nonequilibrium work equalities in isolated quantum systems

doi:10.1088/1674-1056/23/7/070512

中国物理B ›› 2014, Vol. 23 ›› Issue (7): 70512-070512.doi: 10.1088/1674-1056/23/7/070512

所属专题： TOPICAL REVIEW — Statistical Physics and Complex Systems

• TOPICAL REVIEW—Statistical Physics and Complex Systems • 上一篇下一篇

Nonequilibrium work equalities in isolated quantum systems

柳飞^a, 欧阳钟灿^b

a School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China;
b Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China

收稿日期:2014-02-27 修回日期:2014-04-07 出版日期:2014-07-15 发布日期:2014-07-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11174025).

Nonequilibrium work equalities in isolated quantum systems

Liu Fei (柳飞)^a, Ouyang Zhong-Can (欧阳钟灿)^b

a School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China;
b Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China

Received:2014-02-27 Revised:2014-04-07 Online:2014-07-15 Published:2014-07-15
Contact: Ouyang Zhong-Can E-mail:feiliu@buaa.edu.cn
About author:05.70.Ln; 05.30.-d
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11174025).

摘要/Abstract

摘要： We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities in isolated quantum Hamiltonian systems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some results are given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.

关键词: nonequilibrium isolated quantum systems, work equality, probability density function of quantum work, quantum Feynman-Kac formula

Abstract: We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities in isolated quantum Hamiltonian systems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some results are given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.

Key words: nonequilibrium isolated quantum systems, work equality, probability density function of quantum work, quantum Feynman-Kac formula

中图分类号: (Nonequilibrium and irreversible thermodynamics)

05.70.Ln

05.30.-d (Quantum statistical mechanics)

柳飞, 欧阳钟灿. Nonequilibrium work equalities in isolated quantum systems[J]. 中国物理B, 2014, 23(7): 70512-070512.

Liu Fei (柳飞), Ouyang Zhong-Can (欧阳钟灿). Nonequilibrium work equalities in isolated quantum systems[J]. Chin. Phys. B, 2014, 23(7): 70512-070512.

参考文献 121

[1]	Callen H B 1985 Thermodynamics and an Introduction to Thermostatistics (2nd edn.) (New York: John Wiley & Sons, Inc.)
[2]	Jarzynski C 1997 Phys. Rev. Lett. 78 2690
[3]	Jarzynski C 1997 Phys. Rev. E 56 5018
[4]	Liphardt L, Dumont S, Smith S B, Jr Tinoco I and Bustamante C 2002 Science 296 1832
[5]	Collin D, Ritort F, Jarzynski C, Smith S B, Jr Tinoco I and Bustamante C 2005 Nature 437 231
[6]	Douarche F, Ciliberto S and Petrosyan A 2005 J. Stat. Mech.: Theory Exp. P09011
[7]	Bochkov G N and Kuzovlev Yu E 1977 Sov. Phys. JETP 45 125
[8]	Bochkov G N and Kuzovlev Yu E 1977 Zh. Eksp. Teor. Fiz. 72 238
[9]	Bochkov G N and Kuzovlev Yu E 1981 Physica A 106 443
[10]	Bochkov G N and Kuzovlev Yu E 1981 Physica A 106 480
[11]	Callen H B and Welton T A 1951 Phys. Rev. 83 34
[12]	Green M S 1952 J. Chem. Phys. 20 1281
[13]	Kubo R 1966 Rep. Prog. Phys. 29 255
[14]	The current discussion is easily extended into the case with vector driven field.
[15]	Jarzynski C 2007 C. R. Phys. 8 495
[16]	Horowitz J and Jazynski C 2007 J. Stat. Mech.: Theory Exp. P11002
[17]	Evans D J, Cohen E G D and Morriss G P 1993 Phys. Rev. Lett. 71 2401
[18]	Evans D J and Searles D J 1994 Phys. Rev. E 50 1645
[19]	Gallavotti G and Cohen E G D 1995 Phys. Rev. Lett. 74 2694
[20]	Gallavotti G and Cohen E G D 1995 J. Stat. Phys. 80 931
[21]	Kurchan J 1998 J. Phys. A: Math. Gen. 31 3719
[22]	Lebowitz J L and Spohn H 1999 J. Stat. Phys. 95 333
[23]	Crooks G E 1999 Phys. Rev. E 60 2721
[24]	Crooks G E 2000 Phys. Rev. E 61 2361
[25]	Hummer G and Szabo A 2001 Proc. Natl. Acad. Sci. USA 98 3658
[26]	Hatano T and Sasa S I 2001 Phys. Rev. Lett. 86 3463
[27]	Maes C 1999 J. Stat. Phys. 95 367
[28]	Jarzynski C 2004 J. Stat. Mech.: Theory Exp. P09005
[29]	Seifert U 2005 Phys. Rev. Lett. 95 040602
[30]	Speck T and Seifert U 2005 J. Phys. A: Math. Gen. 38 L581
[31]	Kawai R, Parrondo J M R and van den Broeck C 2007 Phys. Rev. Lett. 98 080602
[32]	Esposito M and van den Broeck C 2010 Phys. Rev. Lett. 104 090601
[33]	Sagawa T and Ueda M 2010 Phys. Rev. Lett. 104 090602
[34]	Ritort F 2008 Adv. Chem. Phys. 137 31
[35]	Hänggi P and Marchesoni F 2009 Rev. Mod. Phys. 81 387
[36]	Bustamante C, Liphardt J and Ritort F 2005 Phys. Today 58 43
[37]	Liu Q, Tang C and Ouyang Q 2010 Chin. Phys. B 19 040202
[38]	Piechocinska B 2000 Phys. Rev. A 61 062314
[39]	Kurchan J 2000 arXiv:cond-mat/0007360
[40]	Tasaki H 2000 arXiv:cond-mat/0009244
[41]	Yukawa S 2000 J. Phys. Soc. Jpn. 69 2367
[42]	Mukamel S 2003 Phys. Rev. Lett. 90 170604
[43]	Jarzynski C and Wojcik D K 2004 Phys. Rev. Lett. 92 230602
[44]	De Roeck W and Maes C 2004 Phys. Rev. E 69 026115
[45]	De Roeck W 2007 C. R. Phys. 8 674
[46]	De Roeck W and Maes C 2006 Rev. Math. Phys. 18 619
[47]	Derezinski J, De Roeck W and Maes C 2008 J. Stat. Phys. 131 341
[48]	Talkner P, Lutz E and Hänggi P 2007 Phys. Rev. E 75 050102
[49]	Talkner P and Hänggi P 2007 J. Phys. A: Math. Gen. 40 F569
[50]	Talkner P, Häggi P and Morillo M 2008 Phys. Rev. E 77 051131
[51]	Talkner P, Campisi M and Häggi P 2009 J. Stat. Mech: Theory Exp. P02025
[52]	Campisi M, Talkner P and Hänggi P 2009 Phys. Rev. Lett. 102 210401
[53]	Campisi M, Talkner P and Hänggi P 2010 Phys. Rev. Lett. 105 140601
[54]	Campisi M, Talkner P and Hänggi P 2011 Phil. Trans. R. Soc. A 369 291
[55]	Allahverdyan A E and Nieuwenhuizen T M 2005 Phys. Rev. E 71 066102
[56]	Saito K and Dhar A 2007 Phys. Rev. Lett. 99 180601
[57]	Saito K and Utsumi Y 2008 Phys. Rev. B 78 115429
[58]	Andrieux D and Gaspard P 2008 Phys. Rev. Lett. 100 230404
[59]	Andrieux D, Gaspard P, Monnai T and Tasaki S 2009 New J. Phys. 11 043014
[60]	Crooks G E 2008 Phys. Rev. A 77 034101
[61]	Crooks G E 2008 J. Stat. Mech: Theory Exp. P10023
[62]	Esposito M and Mukamel S 2006 Phys. Rev. E 73 046129
[63]	Esposito M, Harbola U and Mukamel S 2009 Rev. Mod. Phys. 81 1665
[64]	Bunin G, D'Alessio L, Kafri Y and Polkovnikov A 2011 Nat. Phys. 7 913
[65]	Deffner S and Lutz E 2011 Phys. Rev. Lett. 107 140404
[66]	Horowitz J M 2012 Phys. Rev. E 85 031110
[67]	Chetrite R and Mallick K 2012 J. Stat. Phys. 148 480
[68]	Liu F 2012 Phys. Rev. E 86 010103(R)
[69]	Liu F 2012 arXiv:1210.5798 [cond-mat.stat-mech]
[70]	Liu F 2014 Phys. Rev. E 89 042122
[71]	Hekking F W J and Pekola J P 2013 Phys. Rev. Lett. 111 093602
[72]	Horowitz J M and Parrondo J M R 2013 New J. Phys. 15 085028
[73]	Albash T, Lidar D A, Marvian M and Zanardi P 2013 Phys. Rev. E 88 032146
[74]	Leggio B, Napoli A, Messina A and Breuer H P 2013 Phys. Rev. A 88 042111
[75]	Rastegin A E 2013 J. Stat. Mech.: Theory Exp. P06016
[76]	Venkatesh B P, Watanabe G and Talkner P 2014 New J. Phys. 16 015032
[77]	Evans D J and Searles D J 2002 Adv. Phys. 51 1529
[78]	Sevick E M, Prabhakar R, Williams S R and Searles D J 2008 Annu. Rev. Phys. Chem. 59 603
[79]	Jarzynski C 2011 Annu. Rev. Condens. Matter Phys. 2 329
[80]	Seifert U 2012 Rep. Prog. Phys. 75 126001
[81]	Marconi U M B, Puglisi A, Rondoni L and Vulpiani A 2008 Phys. Rep. 461 111
[82]	Campisi M, Hänggi P and Talkner P 2011 Rev. Mod. Phys. 83 771
[83]	Polkovnikov A, Sengupta K, Silva A and Vengalattore M 2011 Rev. Mod. Phys. 83 863
[84]	Batalhao T, Souza A M, Mazzola L, Auccaise R, Sarthour R S, Oliveira I S, Goold J, De Chiara G, Paternostro M and Serra R M 2013 arXiv:1212.5808 [cond-mat.stat-mech]
[85]	Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[86]	Mazzola L, De Chiara G and Paternostro M 2013 Phys. Rev. Lett. 110 230602
[87]	Dorner R, Clark S R, Heaney L, Fazio R, Goold J and Vedral V 2013 Phys. Rev. Lett. 110 230601
[88]	Campisi M, Blattmann R, Kohler S, Zueco D and Hänggi P 2013 New J. Phys. 15 105028
[89]	Mazzola L, De Chiara G and Paternostro M 2014 arXiv:1401.0566 [quant-ph]
[90]	Parrondo J M R, van den Broeck C and Kawai R 2009 New J. Phys. 11 073008
[91]	Chetrite R and Gawedzki K 2008 Commun. Math. Phys. 282 469
[92]	Vaikuntanathan S and Jarzynski C 2009 EPL 87 60005
[93]	Liu F and Ou-Yang Z C 2009 Phys. Rev. E 79 060107(R)
[94]	Liu F, Luo Y P, Huang M C and Ou-Yang Z C 2009 J. Phys. A: Math. Gen. 42 332003
[95]	Liu F, Tong H, Ma R and Ou-Yang Z C 2010 J. Phys. A: Math. Theor. 43 495003
[96]	Liu F and Hong L 2012 J. Phys. A: Math. Gen. 45 125004
[97]	The equality iteself is valid for any physical representation.
[98]	Sakurai J I 1967 Advanced Quantum Mechanics (Reading, Mass.: Addison-Wesly Pub. Co.)
[99]	Feynman R P 1948 Rev. Mod. Phys. 20 367
[100]	Kac M 1949 Trans. Amer. Math. Soc. 65 1
[101]	Hummer G and Szabo A 2001 Proc. Natl. Acad. Sci. USA 98 3658
[102]	Ge H and Jiang D Q 2008 J. Stat. Phys. 131 675
[103]	Stroock D W and Varadhan S R S 1979 Multidimensinal Diffusion Processes (New York: Springer)
[104]	Chaichian M and Demichev A 2001 Path Integrals in Physics: Volume I Stochastic Processes and Quantum Mechanics (Bristol: Institute of Physics Pub.)
[105]	Van Kampen N G 1992 Stochastic Processes in Physics and Chemistry (Amsterdam: North-Holland Physics)
[106]	Engel A and Nolte R 2007 EPL 79 10003
[107]	Deffner S and Lutz E 2008 Phys. Rev. E 77 021128
[108]	Talkner P, Burada P S and Hänggi P 2008 Phys. Rev. E 78 011115
[109]	Wineland D and Dehmelt H 2010 Eur. Phys. J. B 75 275
[110]	Quan H T and Jarzynski C 2012 Phys. Rev. E 85 031102
[111]	Imparato A and Peliti L 2005 Phys. Rev. E 72 046114
[112]	Imparato A and Peliti L 2005 EPL 69 643
[113]	Imparato A and Peliti L 2007 C. R. Phys. 8 556
[114]	Huber G, Schmidt-Kaler F, Deffner S D and Lutz E 2008 Phys. Rev. Lett. 101 070403
[115]	Paul W 1990 Rev. Mod. Phys. 62 531
[116]	Leibfried D, Blatt R, Monroe C and Wineland D 2003 Rev. Mod. Phys. 75 281
[117]	Huber G, Deuschle T, Schnitzler W, Reichle R, Singer K and Schmidt-Kaler F 2008 New J. Phys. 10 013004
[118]	Meekhof D M, Monroe C, King B E, Itano W M and Wineland D J 1996 Phys. Rev. Lett. 76 1796
[119]	Dehmelt H G 1975 Bull. Am. Phys. Soc. 20 60
[120]	Heyl M and Kehrein S 2012 Phys. Rev. Lett. 108 190601
[121]	Pekola J P, Solinas P, Shnirman A and Averin D V 2013 New J. Phys. 15 115006

Nonequilibrium work equalities in isolated quantum systems

Nonequilibrium work equalities in isolated quantum systems

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 121

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Haoguang Liu(刘浩广), Jizhou He(何济洲), and Jianhui Wang(王建辉). Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir[J]. 中国物理B, 2023, 32(3): 30503-030503.
[2]	Xiao-Qiang Su(苏晓强), Zong-Ju Xu(许宗菊), and You-Quan Zhao(赵有权). Entanglement and thermalization in the extended Bose-Hubbard model after a quantum quench: A correlation analysis[J]. 中国物理B, 2023, 32(2): 20506-020506.
[3]	Xiaowen Shen(沈晓文) and Qi Wang(王奇). Thermodynamically consistent model for diblock copolymer melts coupled with an electric field[J]. 中国物理B, 2022, 31(4): 48201-048201.
[4]	Xiu-Xing Zhang(张修兴), Fang-Jv Li(李芳菊), Kai Wang(王凯), Jing Xue(薛晶), Guang-Wen Huo(霍广文), Ai-Ping Fang(方爱平), and Hong-Rong Li(李宏荣). Detection of multi-spin interaction of a quenched XY chain by the average work and the relative entropy[J]. 中国物理B, 2021, 30(9): 90504-090504.
[5]	Yu-Tao Tan(谭宇涛), Lu-Qin Wang(王鲁钦), Zi Wang(王子), Jiebin Peng(彭洁彬), and Jie Ren(任捷). Erratum to “Designing thermal demultiplexer: Splitting phonons by negative mass and genetic algorithm optimization”[J]. 中国物理B, 2021, 30(9): 99902-099902.
[6]	Zhiyuan Lin(林智远), Tong Fu(付彤), Juying Xiao(肖菊英), Shanhe Su(苏山河), Jincan Chen(陈金灿), and Yanchao Zhang(张艳超). Nonequilibrium free energy and information flow of a double quantum-dot system with Coulomb coupling[J]. 中国物理B, 2021, 30(8): 80501-080501.
[7]	. [J]. 中国物理B, 2021, 30(3): 30506-.
[8]	. [J]. 中国物理B, 2021, 30(3): 36301-.
[9]	. [J]. 中国物理B, 2020, 29(12): 120505-.
[10]	. [J]. 中国物理B, 2020, 29(12): 120506-.
[11]	. [J]. 中国物理B, 2020, 29(12): 120504-.
[12]	王晨, 徐大智. A polaron theory of quantum thermal transistor in nonequilibrium three-level systems[J]. 中国物理B, 2020, 29(8): 80504-080504.
[13]	李赫, 杨翔, 张何朋. Symmetry properties of fluctuations in an actively driven rotor[J]. 中国物理B, 2020, 29(6): 60502-060502.
[14]	刘叶锋, 陆金成, 王荣倩, 王晨, 蒋建华. Energy cooperation in quantum thermoelectric systems withmultiple electric currents[J]. 中国物理B, 2020, 29(4): 40504-040504.
[15]	徐酉阳, 刘娟, 冯芒. Fluctuation theorem for entropy production at strong coupling[J]. 中国物理B, 2020, 29(1): 10501-010501.