Convergence of the integral fluctuation theorem estimator for nonequilibrium Markov systems

Year: 2023

Authors: Coghi Francesco; Buffoni Lorenzo; Gherardini Stefano

Autors Affiliation: KTH Royal Inst Technol, Nordita, Hannes Alfvens Vag 12, SE-10691 Stockholm, Sweden; Stockholm Univ, Hannes Alfvens vag 12, SE-10691 Stockholm, Sweden; Portuguese Quantum Inst, P-1049001 Lisbon, Portugal; CNR, Ist Nazl Ott, Area Sci Park, I-34149 Trieste, Italy; Univ Florence, LENS, Via Carrara 1, I-50019 Sesto Fiorentino, Italy.

Abstract: 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.

Journal/Review: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

Volume: 2023 (6)      Pages from: 63201-1  to: 63201-22

More Information: The authors acknowledge The Blanceflor Foundation for financial support through the project Large Deviations approach to Landauer´s Principle (LanDev)´ and the MISTI Global Seed Funds MIT-FVG collaboration grant Non-Equilibrium Thermodynamics of Dissipative Quantum Systems´. We also thank the International Centre for Theoretical Physics (ICTP) in Trieste (Italy) for hospitality during the completion of this work. F C gratefully acknowledges Centre National de la Recherche Scientifique (CNRS) and the Laboratoire de Physique at the ENS Lyon (LPENSL) for hospitality during the writing stage of the manuscript. The authors also warmly thank Hugo Touchette for providing useful comments and suggestions on a first draft of the work.
KeyWords: fluctuation theorems, entropy production, irreversibility, convergence of statistical estimators, nonequilibrium Markov systems, large deviation theory
DOI: 10.1088/1742-5468/acc4b2

Citations: 2
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