Fluctuation Relations for Diffusion Processes

TL;DR

This paper unifies various fluctuation relations for nonequilibrium diffusion processes, linking their origins to different time reversals and extending them to tangent processes for infinitesimal trajectories.

Contribution

It introduces a unified framework for fluctuation relations in diffusion processes, including a multiplicative extension for tangent processes describing close trajectories.

Findings

Unified approach to fluctuation relations for diffusion processes

Identification of time reversal as the origin of different relations

Extension to tangent processes for infinitesimal trajectories

Abstract

The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the time-reversed process. The origin of a variety of fluctuation relations is traced to the use of different time reversals. It is also shown how the application of the presented approach to the tangent process describing the joint evolution of infinitesimally close trajectories of the original process leads to a multiplicative extension of the fluctuation relations.