Linear response theory and transient fluctuation theorems for diffusion processes: a backward point of view

TL;DR

This paper unifies linear response theory and transient fluctuation theorems for diffusion processes using backward equations, revealing their connection to the Markovian property through a generalized Chapman-Kolmogorov equation.

Contribution

It introduces a backward perspective to derive and interpret fluctuation theorems and response theory for diffusion processes, highlighting their fundamental link to Markovian dynamics.

Findings

Transient fluctuation theorems stem from a generalized Chapman-Kolmogorov equation.

Backward equations provide a unified framework for response and fluctuation theorems.

Markovian property underpins the derived fluctuation relations.

Abstract

On the basis of perturbed Kolmogorov backward equations and path integral representation, we unify the derivations of the linear response theory and transient fluctuation theorems for continuous diffusion processes from a backward point of view. We find that a variety of transient fluctuation theorems could be interpreted as a consequence of a generalized Chapman-Kolmogorov equation, which intrinsically arises from the Markovian characteristic of diffusion processes.