Estimating Entropy Production Rates with First-Passage Processes

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.

32 pages, 7 figures, typos have been corrected in the new version

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• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Thermodynamic cost for precision of general counting observables
• Methods and Conversations in (Post)Modern Thermodynamics
• Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation
• Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime
• Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics
• Investigation of radiation-enhanced diffusion using first-passage time
• Martingale approach for first-passage problems of time-additive observables in Markov processes
• Effective Affinity for Generic Currents in Markov Processes
• Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents
• Work statistics at first-passage times
• Multicyclic norias: a first-transition approach to extreme values of the currents
• Concentration of Empirical First-Passage Times
• Experimentally accessible measurement of irreversibility in stochastic systems by categorizing single-molecule displacements
• Thermodynamic inference in molecular motors: a Martingale approach