Fluctuating Entropy Production on the Coarse-Grained Level: Inference and Localization of Irreversibility

TL;DR

This paper develops a framework linking trajectory-based entropy production with coarse-grained dynamics, enabling localization and inference of irreversibility in small systems, including underdamped Langevin dynamics.

Contribution

It introduces a unified approach to entropy production in coarse-grained systems using snippets and Markovian events, facilitating the detection of hidden driving forces.

Findings

Framework applies to even and odd variables.

Enables localization of entropy contributions in time and space.

Supports inference of hidden driving in stochastic systems.

Abstract

Stochastic thermodynamics provides the framework to analyze thermodynamic laws and quantities along individual trajectories of small but fully observable systems. If the observable level fails to capture all relevant degrees of freedom, some form of effective, coarse-grained dynamics naturally emerges for which the principles of stochastic thermodynamics generally cease to be applicable straightforwardly. Our work unifies the notion of entropy production along an individual trajectory with that of a coarse-grained dynamics by establishing a framework based on snippets and Markovian events as fundamental building blocks. A key asset of a trajectory-based fluctuating entropy production is the ability to localize individual contributions to the total entropy production in time and space. As an illustration and potential application for inference we introduce a method for the detection of hidden driving. The framework applies equally to even and odd variables and, therefore, includes the peculiar case of entropy production in underdamped Langevin dynamics.