Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter

TL;DR

This paper introduces a framework to quantify irreversibility in active matter systems by evaluating entropy production in coarse-grained models, revealing spatial structures and deviations from equilibrium.

Contribution

It develops methods to measure and analyze entropy production in scalar field theories of active matter, including local and spectral decompositions and a generalized Harada-Sasa relation.

Findings

Entropy production concentrates at interfaces in phase-separated states.

In homogeneous states, entropy production relates to fluctuation-dissipation deviations.

The framework distinguishes equilibrium from active non-equilibrium behavior.

Abstract

Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: it vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles without alignment interactions, capturing such key phenomena as motility-induced phase separation. We show how the entropy production can be decomposed locally (in real space) or spectrally (in Fourier space), allowing detailed examination of the spatial structure and correlations that underly departures from equilibrium. For phase-separated systems, the local entropy production is concentrated mainly on interfaces with a bulk contribution that tends to zero in the weak-noise limit. In homogeneous states, we find a generalized Harada-Sasa relation that directly expresses the entropy production in terms of the wavevector-dependent deviation from the fluctuation-dissipation relation between response functions and correlators. We discuss extensions to the case where the particle density is coupled to a momentum-conserving solvent, and to situations where the particle current, rather than the density, should be chosen as the dynamical field. We expect the new conceptual tools developed here to be broadly useful in the context of active matter, allowing one to distinguish when and where activity plays an essential role in the dynamics.