Entropy bound for time reversal markers

TL;DR

This paper establishes an entropy production bound using path-antisymmetric observables, especially the signum of entropy, facilitating easier estimation and coarse graining, with demonstrated saturation in driven ring networks.

Contribution

It introduces a new entropy bound based on path-antisymmetric observables and shows how to preserve it under coarse graining, advancing systematic entropy analysis.

Findings

The optimal observable for the bound is the signum of entropy production.

The bound saturates for short times in driven ring networks.

The method enables systematic coarse graining of entropy production.

Abstract

We derive a bound for entropy production in terms of the mean of normalizable path-antisymmetric observables. The optimal observable for this bound is shown to be the signum of entropy production, which is often easier determined or estimated than entropy production itself. It can be preserved under coarse graining by use of a simple path grouping algorithm. We demonstrate this relation and its properties using a driven network on a ring, for which the bound saturates for short times for any driving strength. This work can open a way to systematic coarse graining of entropy production.