Time-resolved statistics of snippets as general framework for model-free entropy estimators

TL;DR

This paper introduces a versatile framework for estimating entropy production by analyzing time-resolved statistics of trajectory snippets, including symmetric events, with a focus on Markovian properties and detailed balance relations.

Contribution

It presents a novel, model-free method to infer lower bounds on entropy production using snippets of trajectories and a new criterion for Markovianity based on event properties.

Findings

Framework allows entropy estimation from time-resolved event statistics.

Operational criterion for Markovianity based on event properties.

Generalized detailed balance relation for trajectory snippets.

Abstract

Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia, allows us to infer a lower bound on entropy production through measuring the time-resolved statistics of events with any symmetry under time-reversal, in particular, time-symmetric instantaneous events. We emphasize Markovianity as a property of certain events rather than of the full system and introduce an operationally accessible criterion for this weakened Markov property. Conceptually, the approach is based on snippets as particular sections of trajectories, for which a generalized detailed balance relation is discussed.