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   

  1. 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)   

  1. 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: 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)