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

Abstract

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.

35 pages

References in corpus (11)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Fluctuations and response of nonequilibrium states
• An Extension of the Fluctuation Theorem
• An update on nonequilibrium linear response
• Fluctuation Relations for Diffusion Processes
• Nonlinear response and fluctuation dissipation relations
• Relaxation rates of gene expression kinetics reveal the feedback signs of autoregulatory gene networks
• Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables
• Model simplification and loss of irreversibility
• Asymptotics of Sample Entropy Production Rate for Stochastic Differential Equations

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