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Cavity optomechanical systems are a paradigmatic setting for the conversionof electromagnetic energy into mechanical work. Experiments with atoms coupledto cavity modes are realized in nonequilibrium conditions, described byphenomenological models encoding non-thermal dissipative dynamics and fallingoutside the framework of weak system-bath couplings. This fact makes theirinterpretation as quantum engines, e.g., the derivation of a well-definedefficiency, quite challenging. Here, we present a consistent thermodynamicdescription of open quantum cavity-atom systems. Our approach takes advantageof their nonequilibrium nature and arrives at an energetic balance which isfully interpretable in terms of persistent dissipated heat currents. Theinteraction between atoms and cavity modes can further give rise tononequilibrium phase transitions and emergent behavior and allows to assess theimpact of collective many-body phenomena on the engine operation. To enablethis, we define two thermodynamic limits related to a weak and to a strongoptomechanical coupling, respectively. We illustrate our ideas focussing on atime-crystal engine and discuss power generation, energy-conversion efficiency,and emergence of metastable behavior in both limits.

Nonequilibrium thermodynamics and power generation in open quantum optomechanical systems