Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Chen, Xian¹  Jia, Chen² 

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

关键词: Stochastic thermodynamics;    Linear response;    Fluctuation relation;    Nonsymmetric Markov process;    Stochastic differential equation;    Parabolic equation;   

DOI  :  10.1016/j.spa.2019.02.005

来源: Elsevier

【 摘 要 】

Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for inhomogeneous diffusion processes with unbounded drift and diffusion coefficients by using the Schauder estimates for partial differential equations of parabolic type and the theory of weakly continuous semigroups. The FDTs proved in this paper apply to any forms of inhomogeneous and nonlinear external perturbations. Furthermore, we prove the uniqueness of the conjugate observables and clarify the precise mathematical conditions and ranges of applicability for the two types of FDTs. Examples are also given to illustrate the main results of this paper. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free