Heat, temperature and Clausius inequality in a model for active brownian particles

TL;DR

This paper applies stochastic thermodynamics and hydrodynamics to a model of active particles with Gaussian coloured noise, deriving heat, work, entropy production, and a Clausius inequality involving local temperature, and explores hydrodynamic limits and approximations.

Contribution

It introduces a thermodynamic and hydrodynamic framework for active particles with coloured noise, deriving new inequalities and conditions beyond existing models.

Findings

Clausius inequality with local active bath temperature

Hydrodynamic equations with pressure, temperature, and heat flux

Conditions under which UCNA yields detailed balance

Abstract

Methods of stochastic thermodynamics and hydrodynamics are applied to the a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system's Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.