  We propose 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 main idea is to consider joint
trajectories of particles' positions and self-propulsions. It is then possible
to exploit 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, $\Delta s_\text{tot}$, can be decomposed into housekeeping, $\Delta
s_\text{hk}$, and excess, $\Delta s_\text{ex}$, parts. Both $\Delta
s_\text{tot}$ and $\Delta s_\text{hk}$ 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. Interestingly,
although the evolution of particles' self-propulsions is free and uncoupled
from that of their positions, non-trivial steady-state correlations between
these variables lead to the non-zero excess dissipation in the reservoir
coupled to the self-propulsions.
