Estimating entropy production rates with first-passage processes

Abstract We consider the problem of estimating mean entropy production rate in a nonequilibrium process from measurements first-passage quantities associated with single current. For processes large thresholds, references (Roldán et al 2015 Phys. Rev. Lett. 115 250602; Neri 2022 SciPost 12 139) identified ratio observables—involving time, splitting probability, and thresholds—that lower bounds is an unbiased estimator when applied to current that proportional stochastic production. Here, we show also at finite number realisations process, for currents are not production, ratios can accurately estimate dissipation. In particular, capture fraction total regimes far thermal equilibrium where thermodynamic uncertainty negligible rate. Moreover, incorporate nonMarkovian statistics estimated value dissipation rate, which difficult include estimates based on Kullback–Leibler divergences. Taken together, estimation complements well methods