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Waiting-time-based entropy estimators in continuous space without Markovian events

Jonas H. Fritz and Udo Seifert

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Phys. Rev. E 114, 034109 – Published 4 September, 2026

DOI: https://doi.org/10.1103/zj2b-w93z

Abstract

Estimating entropy production in continuous systems that can only be observed with a limited resolution remains an open problem in stochastic thermodynamics. Existing estimators based on the measurement of waiting-time distributions either require the detection of Markovian events, which uniquely determine the state of the system, or assume a discrete underlying dynamics. We present a novel estimator that relies solely on the detection of a single particle leaving or entering regions, or crossing manifolds, in continuous space. This estimator is based on the frequency and the duration of transitions between such events. We derive this bound by introducing two kinds of discretization of space. Finally, we compare our novel bound to the thermodynamic uncertainty relation improved by correlations using simulations of a Brownian vortex, and we discuss its relation to other lower bounds to entropy production.

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Phys. Rev. E 114, 034109– Published 4 September, 2026
  • Received 5 March 2026
  • Accepted 12 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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