Convergence of the integral fluctuation theorem estimator for nonequilibrium Markov systems. (English) Zbl 1539.60024
Summary: The integral fluctuation theorem (IFT) for entropy production 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.
{© 2023 The Author(s). Published on behalf of SISSA Medialab srl by IOP Publishing Ltd}
{© 2023 The Author(s). Published on behalf of SISSA Medialab srl by IOP Publishing Ltd}
MSC:
| 60F10 | Large deviations |
| 62M05 | Markov processes: estimation; hidden Markov models |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
| 62G20 | Asymptotic properties of nonparametric inference |
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
Keywords:
fluctuation theorems; entropy production; irreversibility; convergence of statistical estimators; nonequilibrium Markov systems; large deviation theoryReferences:
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