Entropy Production from Density Field Theories for interacting particles systems

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.

💡 Research Summary

The paper tackles the fundamental problem of quantifying time‑reversal symmetry breaking in interacting particle systems by deriving explicit, closed‑form expressions for entropy production directly from density‑field theories. Starting from Dean’s exact stochastic partial differential equation for the microscopic density of N interacting Langevin particles, the authors incorporate non‑conservative forces and formulate the dynamics in the Itô convention. By introducing an Onsager‑Machlup (OM) path‑integral representation of the stochastic dynamics, they obtain a functional action A