Integral Fluctuation Theorems for Stochastic Resetting Systems

TL;DR

This paper derives two integral fluctuation theorems for stochastic resetting systems, revealing fundamental thermodynamic relations despite violations of microreversibility, and recovers a second law-like inequality.

Contribution

It introduces two new integral fluctuation theorems applicable to resetting systems, extending stochastic thermodynamics to non-microreversible dynamics.

Findings

Resetting systems satisfy two integral fluctuation theorems.

The second law-like inequality is derived from the second fluctuation theorem.

The theorems hold despite violations of microreversibility.

Abstract

We study the stochastic thermodynamics of resetting systems. Violation of microreversibility means that the well known derivations of fluctuations theorems break down for dynamics with resetting. Despite that we show that stochastic resetting systems satisfy two integral fluctuation theorems. The first is the Hatano-Sasa relation describing the transition between two steady states. The second integral fluctuation theorem involves a functional that includes both dynamical and thermodynamic contributions. We find that the second law-like inequality found by Fuchs et al. for resetting systems [EPL, 113, (2016)] can be recovered from this integral fluctuation theorem with the help of Jensen's inequality.