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

TL;DR

This paper introduces a new entropy estimator for continuous systems that only requires detecting particle transitions across regions, avoiding the need for Markovian event detection or discrete dynamics assumptions.

Contribution

The authors develop a novel entropy estimator based on transition frequencies and durations, applicable in continuous space without Markovian event detection.

Findings

Estimator performs well in Brownian vortex simulations

Provides a lower bound on entropy production without Markovian assumptions

Compared favorably to the TUR and other bounds in tests

Abstract

Estimating entropy production in continuous systems that can only be observed with a limited resolution remains an open problem in stochastic thermodynamics. Extant estimators based on the measurement of waiting-time distributions require either 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 TUR using simulations of a Brownian vortex and discuss its relation to other lower bounds to entropy production.