Estimating Entropy Production Rates with First-Passage Processes

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 thresh- olds, references (Roldán et al 2015 Phys. Rev. Lett. 115 250602; Neri 2022 SciPost Phys. 12 139) 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 pro- duction, 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 is difficult to include in estimates based on Kullback–Leibler divergences. Taken together, we show that entropy production estimation with first-passage ratios comple- ments well estimation methods based on thermodynamic uncertainty ratios and Kullback–Leibler divergences.