Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems

TL;DR

This paper develops methods to estimate the Kullback-Leibler divergence between stationary trajectories of discrete systems, linking it to entropy production and analyzing the accuracy of these estimators in physical models.

Contribution

It introduces analytical and numerical techniques to estimate KLD in discrete stochastic systems and explores their relation to entropy production.

Findings

Estimators accurately quantify KLD in discrete systems.

KLD provides a lower bound to entropy production.

Sampling more degrees of freedom improves estimation accuracy.

Abstract

The irreversibility of a stationary time series can be quantified using the Kullback-Leibler divergence (KLD) between the probability to observe the series and the probability to observe the time-reversed series. Moreover, this KLD is a tool to estimate entropy production from stationary trajectories since it gives a lower bound to the entropy production of the physical process generating the series. In this paper we introduce analytical and numerical techniques to estimate the KLD between time series generated by several stochastic dynamics with a finite number of states. We examine the accuracy of our estimators for a specific example, a discrete flashing ratchet, and investigate how close is the KLD to the entropy production depending on the number of degrees of freedom of the system that are sampled in the trajectories.