Measurement of irreversibility and entropy production via the tubular ensemble

TL;DR

This paper introduces a practical method to measure irreversibility and entropy production in stochastic processes by regularizing trajectory probabilities within tubular neighborhoods, enabling experimental and model-free analysis of irreversibility.

Contribution

It proposes a novel regularization approach to estimate entropy production from measurable trajectory probabilities, aligning with stochastic thermodynamics and applicable to short recorded trajectories.

Findings

Excellent agreement with theoretical predictions for Langevin dynamics.

Method enables pathwise irreversibility measurement in experiments.

Infers entropy-production distribution from short trajectory data.

Abstract

The appealing theoretical measure of irreversibility in a stochastic process, as the ratio of the probabilities of a trajectory and its time reversal, cannot be accessed directly in experiment since the probability of a single trajectory is zero. We regularize this definition by considering, instead, the limiting ratio of probabilities for trajectories to remain in the tubular neighborhood of a smooth path and its time reversal. The resulting pathwise medium entropy production agrees with the formal expression from stochastic thermodynamics, and can be obtained from measurable tube probabilities. Estimating the latter from numerically sampled trajectories for Langevin dynamics yields excellent agreement with theory. By combining our measurement of pathwise entropy production with a Markov Chain Monte Carlo algorithm, we infer the entropy-production distribution for a transition path ensemble directly from short recorded trajectories. Our work enables the measurement of irreversibility along individual paths, and path ensembles, in a model-free manner.