Waiting for rare entropic fluctuations

TL;DR

This paper investigates the distribution of first passage times for entropy production in non-equilibrium stochastic systems, revealing how fluctuation relations influence the asymptotic behavior and connecting mean residence times to system currents.

Contribution

It introduces the analysis of first passage time distributions for entropy production, highlighting the role of fluctuation relations in the time domain, which is a novel perspective.

Findings

Fluctuation relation symmetry governs the asymptotic behavior of FPTD.

Mean residence time relates to particle current and steady state distribution.

FPTD exhibits symmetry properties similar to fluctuation relations.

Abstract

Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the distribution of these observables, at large fixed time. To characterize the precise stochastic nature of the process, we here address the distribution in the time domain. In particular, we focus on the first passage time distribution (FPTD) of entropy production, in several realistic models. We find that the fluctuation relation symmetry plays a crucial role in getting the typical asymptotic behavior. Similarities and differences to the simple random walk picture are discussed. For a driven particle in the ring geometry, the mean residence time is connected to the particle current and the steady state distribution, and it leads to a fluctuation relation-like symmetry in terms of the FPTD.