Cycle symmetry, limit theorems, and fluctuation theorems for diffusion processes on the circle

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Ge, Hao^1,2  Jia, Chen^3,4  Jiang, Da-Quan^3,5 

[1] Peking Univ, Biodynam Opt Imaging Ctr, Beijing 100871, Peoples R China

[2] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

[3] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

[4] Univ Texas Dallas, Dept Math Sci, Richardson, TX 75080 USA

[5] Peking Univ, Ctr Stat Sci, Beijing 100871, Peoples R China

关键词: Excursion theory;    Bessel process;    Haldane equality;    Cycle flux;    Nonequilibrium;   

DOI  :  10.1016/j.spa.2016.09.011

来源: Elsevier

【 摘 要 】

Cyclic structure and dynamics are of great interest in both the fields of stochastic processes and nonequilibrium statistical physics. In this paper, we find a new symmetry of the Brownian motion named as the quasi-time-reversal invariance. It turns out that such an invariance of the Brownian motion is the key to prove the cycle symmetry for diffusion processes on the circle, which says that the distributions of the forming times of the forward and backward cycles, given that the corresponding cycle is formed earlier than the other, are exactly the same. With the aid of the cycle symmetry, we prove the strong law of large numbers, functional central limit theorem, and large deviation principle for the sample circulations and net circulations of diffusion processes on the circle. The cycle symmetry is further applied to obtain various types of fluctuation theorems for the sample circulations, net circulation, and entropy production rate. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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