Extended Thermodynamic Relation and Fluctuation Theorem in Stochastic Dynamics with Time Reversed Process

TL;DR

This paper develops an extended thermodynamic relation for stochastic dynamics with time-reversed processes and derives fluctuation theorems like Jarzynski and Seifert relations using averaged quantities.

Contribution

It introduces an extended thermodynamic framework for stochastic systems with forward and backward time processes, deriving new fluctuation theorems.

Findings

Derived the Seifert fluctuation relation for averaged quantities.

Established the Jarzynski equality in the context of the extended thermodynamic relation.

Connected non-equilibrium steady states with fluctuation theorems.

Abstract

We consider a stochastic model described by two stochastic differential equations of motion; one is for the stochastic evolution forward in time and the other for backward in time. We further introduce averaged quantities for the two processes and construct the extended thermodynamic relation following the strategy of Sekimoto. By using this relation, we derive the fluctuation theorems such as the Seifert relation, the Jarzynski relation and the Komatsu-Nakagawa non-equilibrium steady state with respect to the introduced averaged quantities.