Posterior probability and fluctuation theorem in stochastic processes

TL;DR

This paper introduces a generalized fluctuation theorem for stochastic processes using posterior probabilities, removing the need for microscopic reversibility and unifying several known theorems under a broader framework.

Contribution

It proposes a new fluctuation theorem based on posterior probabilities that does not require microscopic reversibility, extending the applicability of fluctuation relations.

Findings

Recovers the Gallavotti-Cohen fluctuation theorem

Derives the Jarzynski equality as a special case

Unifies various fluctuation theorems under a generalized framework

Abstract

A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via the Bayes theorem. In usual fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem adequately recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when adequate assumptions are employed.