  Cavity optomechanical systems are a paradigmatic setting for the conversion
of electromagnetic energy into mechanical work. Experiments with atoms coupled
to cavity modes are realized in nonequilibrium conditions, described by
phenomenological models encoding non-thermal dissipative dynamics and falling
outside the framework of weak system-bath couplings. This fact makes their
interpretation as quantum engines, e.g., the derivation of a well-defined
efficiency, quite challenging. Here, we present a consistent thermodynamic
description of open quantum cavity-atom systems. Our approach takes advantage
of their nonequilibrium nature and arrives at an energetic balance which is
fully interpretable in terms of persistent dissipated heat currents. The
interaction between atoms and cavity modes can further give rise to
nonequilibrium phase transitions and emergent behavior and allows to assess the
impact of collective many-body phenomena on the engine operation. To enable
this, we define two thermodynamic limits related to a weak and to a strong
optomechanical coupling, respectively. We illustrate our ideas focussing on a
time-crystal engine and discuss power generation, energy-conversion efficiency,
and emergence of metastable behavior in both limits.
