Stochastic thermodynamics for self-propelled particles

We present a generalization of stochastic thermodynamics to systems of active particles, which move under the combined influence of stochastic internal self-propulsions (activity) and a heat bath. The generalization relies upon a formal similarity of an active system and a system consisting of two subsystems interacting with different heat reservoirs and coupled by a non-symmetric interaction. The resulting thermodynamic description closely follows the standard stochastic thermodynamics. In particular, total entropy production, Δs_tot, can be decomposed into housekeeping, Δs_hk, and excess, Δs_ex, parts. Both Δs_tot and Δs_hk satisfy fluctuation theorems. The average rate of the steady-state housekeeping entropy production can be related to the violation of the fluctuation-dissipation theorem via a Harada-Sasa relation. The excess entropy production enters into a Hatano-Sasa-like relation, which leads to a generalized Clausius inequality involving the change of the system's entropy and the excess entropy production.