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.Comment: 19 pages, 1 figure. Major changes in the text. 1 figure has been
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