Mathematical foundation of nonequilibrium fluctuationdissipation theorems for inhomogeneous diffusion processes with unbounded coefficients
Abstract
Nonequilibrium fluctuationdissipation 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2017
 DOI:
 10.48550/arXiv.1708.09744
 arXiv:
 arXiv:1708.09744
 Bibcode:
 2017arXiv170809744C
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Mathematics  Probability;
 60J60;
 82C05;
 60H10;
 82C31;
 35K10
 EPrint:
 35 pages