Nonequilibrium thermodynamics and fluctuation relations for small systems

doi:10.1088/1674-1056/23/7/070501

中国物理B ›› 2014, Vol. 23 ›› Issue (7): 70501-070501.doi: 10.1088/1674-1056/23/7/070501

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 thermodynamics and fluctuation relations for small systems

曹亮, 柯谱, 乔丽颜, 郑志刚

Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Studies, Beijing Normal University, Beijing 100875, China

收稿日期:2014-01-20 修回日期:2014-03-03 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. 11075016) and the Foundation for Doctoral Training from the Ministry of Education of China (Grant No. 20100003110007).

Nonequilibrium thermodynamics and fluctuation relations for small systems

Cao Liang (曹亮), Ke Pu (柯谱), Qiao Li-Yan (乔丽颜), Zheng Zhi-Gang (郑志刚)

Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Studies, Beijing Normal University, Beijing 100875, China

Received:2014-01-20 Revised:2014-03-03 Online:2014-07-15 Published:2014-07-15
Contact: Zheng Zhi-Gang E-mail:zgzheng@bnu.edu.cn
About author:05.20.-y; 05.40.-a; 05.70.Ln
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11075016) and the Foundation for Doctoral Training from the Ministry of Education of China (Grant No. 20100003110007).

摘要/Abstract

摘要： In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become significant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti-Cohen fluctuation theorem, and then to the Evans-Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluctuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.

关键词: free-energy equality, fluctuation theorem, Markov process, detailed balance

Abstract: In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become significant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti-Cohen fluctuation theorem, and then to the Evans-Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluctuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.

Key words: free-energy equality, fluctuation theorem, Markov process, detailed balance

中图分类号: (Classical statistical mechanics)

05.20.-y

05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 05.70.Ln (Nonequilibrium and irreversible thermodynamics)

曹亮, 柯谱, 乔丽颜, 郑志刚. Nonequilibrium thermodynamics and fluctuation relations for small systems[J]. 中国物理B, 2014, 23(7): 70501-070501.

Cao Liang (曹亮), Ke Pu (柯谱), Qiao Li-Yan (乔丽颜), Zheng Zhi-Gang (郑志刚). Nonequilibrium thermodynamics and fluctuation relations for small systems[J]. Chin. Phys. B, 2014, 23(7): 70501-070501.

参考文献 44

[1]	Boltzmann L 1964 Lectures on Gas Theory (English transl. by SG Brush) (California: University of California)
[2]	Gibbs J W 1981 Elementary Principles in Statistical Mechanics (Boson: Yale University)
[3]	Landau L D and Lifshitz E M 1986 Statistical Physics (New York: Pergamon)
[4]	Plischke M and Bergersen B 2006 Equilibrium Statistical Physics (Singapore: World Scientific)
[5]	Glansdorff P and Prigogine I 1971 Thermodynamic Theory of Structure, Stability, and Fluctuations (New York: Wiley-Interscience)
[6]	Lebowitz L 1993 Physics Today 46 32,
[7]	Kubo R 1966 Rep. Prog. Phys. 29 255
[8]	Kubo R, Toda M and Hashitsume N 1995 Statistical Physics Ⅱ : Nonequilibrium Statistical Mechanics (2nd edn.) (Berlin: Springer-Verlag)
[9]	Cohen E G D, Evans D J and Morriss G P 1993 Phys. Rev. Lett. 71 2401
[10]	Sinai Y 1977 Lectures in Ergodic Theory (Princeton: Princeton University)
[11]	Eckmann J and Ruelle D 1985 Rev. Mod. Phys. 57 617
[12]	Gallavotti G and Cohen E G D 1995 Phys. Rev. Lett. 74 2694
[13]	Gallavotti G and Cohen E G D 1995 J. Stat. Phys. 80 931
[14]	Evans D J and Searles D J 1994 Phys. Rev. E 50 1645
[15]	Jarzynski C 1997 Phys. Rev. Lett. 78 2690
[16]	Jarzynski C 1997 Phys. Rev. E 56 5018
[17]	Crooks G E 1998 J. Stat. Phys. 90 1481
[18]	Crooks G E 1999 Phys. Rev. E 60 2721
[19]	Zheng Z G 2004 Spatiotemporal Dynamics and Collective Behaviours in Coupled System (Beijing: Higher Education Press) (in Chinese)
[20]	Anosov D V 1967 Proc. Steklov Inst. Mathematics 90 3
[21]	Ott E 2002 Chaos in Dynamical Systems (Cambridge: Cambridge University Press)
[22]	http://fibonacci.math.uri.edu/ kulenm/diffeqaturi/victor442/index.html
[23]	Evans D J and Searles D J 2002 Adv. Phys. 51 1529
[24]	Evans D J 2003 Molecular Phys. 101 1551,
[25]	Searles D J and Evans D J 2004 Aust. J. Chem. 57 1119,
[26]	Williams S R, Sevick E M, Prabhakar R and Searles D J 2008 Annu. Rev. Phys. Chem. 59 603
[27]	Searles D J, Evans D J and Williams S R 2010 J. Chem. Phys. 132 024501
[28]	Liphardt J, Bustamante C and Ritort F 2005 Physics Today 58 43
[29]	Jarzynski C 2011 Annu. Rev. Condens. Matter Phys. 2 329
[30]	Crooks G E 2000 Phys. Rev. E 61 2361
[31]	Klein M J 1955 Phys. Rev. 97 1446
[32]	Crooks G E and Jarzynski C 2007 Phys. Rev. E 75 021116
[33]	Feng E H and Crooks G E 2008 Phys. Rev. Lett. 101 090602
[34]	Jarzynski C 2004 J. Stat. Mech. P09005
[35]	Williams S R, Searles D J and Evans D J 2008 Phys. Rev. Lett. 100 250601
[36]	Chatelain C 2007 J. Stat. Mech. P04011
[37]	Chelli R 2009 J. Chem. Phys. 130 054102
[38]	Cao L, Cross M and Zheng Z 2012 Chin. Phys. B 21 090501
[39]	Hanggi P 1977 Z. Phys. B 26 85
[40]	Hanggi P and Thomas H 1982 Phys. Rep. 88 207
[41]	Hanggi P and Jung P 1995 Advances in Chem. Phys. 89 239
[42]	Mai T and Dhar A 2007 Phys. Rev. E 75 061101
[43]	Speck T and Seifert U 2007 J. Stat. Mech. L09002
[44]	Cao L, Cross M and Zheng Z 2013 unpublished

Nonequilibrium thermodynamics and fluctuation relations for small systems

Nonequilibrium thermodynamics and fluctuation relations for small systems

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