Testing the irreversibility of a Gibbsian process via hitting and return times

TL;DR

This paper develops statistical estimators for entropy production in Gibbsian processes using hitting and return times, enabling tests for process irreversibility based on trajectory observations.

Contribution

It introduces novel estimators for entropy production in Gibbsian processes and analyzes their convergence and fluctuation properties for irreversibility testing.

Findings

Estimators effectively measure entropy production from trajectory data.

Convergence and fluctuation properties are rigorously analyzed.

Provides statistical tests for process irreversibility.

Abstract

We introduce estimators for the entropy production of a Gibbsian process based on the observation of a single or two typical trajectories. These estimators are built with adequate hitting and return times. We then study their convergence and fluctuation properties. This provides statisticals test for the irreversibility of Gibbsian processes.