Nonequilibrium thermodynamics and fluctuation relations for small systems

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

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.

Keywords: free-energy equality fluctuation theorem Markov process detailed balance

Received: 20 January 2014
Revised: 03 March 2014
Accepted manuscript online:

PACS:	05.20.-y	(Classical statistical mechanics)
	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)
	05.70.Ln	(Nonequilibrium and irreversible thermodynamics)

Fund: 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).

Corresponding Authors: Zheng Zhi-Gang
E-mail: zgzheng@bnu.edu.cn

About author: 05.20.-y; 05.40.-a; 05.70.Ln

Cite this article:

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 2014 Chin. Phys. B 23 070501

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