Entropy Production from Density Field Theories for interacting particles systems

TL;DR

This paper introduces a new method to calculate entropy production in density functional theories for interacting particle systems, enabling analysis of irreversibility in complex non-equilibrium active matter models.

Contribution

It develops a tractable, path-integral based approach to quantify entropy production across various density field theories, including active and non-reciprocal systems.

Findings

Reproduces particle-level entropy calculations

Matches recent Doi-Peliti treatments

Extends to active mixtures and suspensions

Abstract

Entropy production quantifies the breaking of time-reversal symmetry in non-equilibrium systems. Here, we develop a direct method to obtain closed, tractable expressions for entropy production in a broad class of dynamical density functional theories, from Dean's exact stochastic equation for microscopic densities to coarse-grained fluctuating-hydrodynamics models with density-dependent mobility. The method employs an Onsager-Machlup path-integral formulation. Our results reproduce particle-level calculations and matches recent Doi-Peliti treatments, confirming that the irregular noise structure of Dean's equation poses no obstacle when handled consistently. We further extend the framework to active mixtures with non-reciprocal interactions and to run-and-tumble or active-Brownian suspensions, generalizations that require a careful treatment of the spurious-drift. Our method furnishes a practical route to quantify irreversibility in density functional field theories and paves the way for systematic studies of entropy production in multi-field active fluids that couple density, momentum and orientation.