Fluctuation relations for a driven Brownian particle

TL;DR

This paper derives a general fluctuation relation for a driven Brownian particle, linking path probabilities to entropy flux, unifying several known fluctuation theorems in different special cases.

Contribution

It introduces a comprehensive fluctuation relation for driven Brownian particles that encompasses existing theorems as special cases.

Findings

Derivation of a general fluctuation relation involving entropy flux.

Unification of Seifert, Jarzynski, and Gallavotti-Cohen fluctuation theorems.

Applicable to systems with conservative and non-conservative forces.

Abstract

We consider a driven Brownian particle, subject to both conservative and non-conservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski and Gallavotti-Cohen in different special cases.