Entropy production from density field theories for interacting particles systems

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 match 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. is a first step towards the systematic studies of entropy production in multi-field active fluids that couple density, momentum and orientation.