Convergence of the Integral Fluctuation Theorem estimator for nonequilibrium Markov systems

TL;DR

This paper investigates the convergence properties of the Integral Fluctuation Theorem estimator in nonequilibrium Markov systems, highlighting limitations, proposing experimental setup strategies, and demonstrating improvements through examples.

Contribution

It introduces a method to identify parameter regions where the IFT estimator converges reliably and suggests ways to enhance convergence for finite correlation time Markov chains.

Findings

Identified limitations of the IFT estimator in sampling rare events.

Proposed a parameter setup method for safe estimator convergence.

Showed improved convergence for Markov chains with finite correlation time.

Abstract

The Integral Fluctuation Theorem for entropy production (IFT) is among the few equalities that are known to be valid for physical systems arbitrarily driven far from equilibrium. Microscopically, it can be understood as an inherent symmetry for the fluctuating entropy production rate implying the second law of thermodynamics. Here, we examine an IFT statistical estimator based on regular sampling and discuss its limitations for nonequilibrium systems, when sampling rare events becomes pivotal. Furthermore, via a large deviation study, we discuss a method to carefully setup an experiment in the parameter region where the IFT estimator safely converges and also show how to improve the convergence region for Markov chains with finite correlation time. We corroborate our arguments with two illustrative examples.