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 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.

23 pages

References in corpus (24)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Motility-Induced Phase Separation
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• How far from equilibrium is active matter?
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Entropy production as correlation between system and reservoir
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Classical dynamical density functional theory: from fundamentals to applications
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter
• Statistical mechanics for non-reciprocal forces
• Cluster phases and bubbly phase separation in active fluids: Reversal of the Ostwald process
• Entropy production of active particles and for particles in active baths
• Non-reciprocity across scales in active mixtures
• Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey
• Rules of calculus in the path integral representation of white noise Langevin equations: the Onsager-Machlup approach
• Effective action for stochastic partial differential equations
• Entropy production in exactly solvable systems
• Critical active dynamics is captured by a colored-noise driven field theory
• Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production
• Particle Entity in the Doi-Peliti and Response Field Formalisms