Estimating Entropy Production Rates with First-Passage Processes

TL;DR

This paper introduces a method using first-passage ratios to accurately estimate entropy production rates in nonequilibrium processes, even at finite thresholds and for non-proportional currents, capturing dissipation more effectively than existing methods.

Contribution

It demonstrates that first-passage ratios can reliably estimate entropy production in finite conditions and regimes far from equilibrium, incorporating non-Markovian effects.

Findings

First-passage ratios estimate a significant fraction of entropy production.

They remain accurate at finite thresholds and for non-proportional currents.

They incorporate non-Markovian statistics, unlike other methods.

Abstract

We consider the problem of estimating the mean entropy production rate in a nonequilibrium process from the measurements of first-passage quantities associated with a single current. For first-passage processes with large thresholds, Refs. [1, 2] identified a ratio of first-passage observables - involving the mean first-passage time, the splitting probability, and the first-passage thresholds - that lower bounds the entropy production rate and is an unbiased estimator of the entropy production rate when applied to a current that is proportional to the stochastic entropy production. Here, we show that also at finite thresholds, a finite number of realisations of the nonequilibrium process, and for currents that are not proportional to the stochastic entropy production, first-passage ratios can accurately estimate the rate of dissipation. In particular, first-passage ratios capture a finite fraction of the total entropy production rate in regimes far from thermal equilibrium where thermodynamic uncertainty ratios capture a negligible fraction of the total entropy production rate. Moreover, we show that first-passage ratios incorporate nonMarkovian statistics in the estimated value of the dissipation rate, which are difficult to include in estimates based on Kullback-Leibler divergences. Taken together, we show that entropy production estimation with first-passage ratios is complementary to estimation methods based on thermodynamic uncertainty ratios and Kullback-Leibler divergences.