Quantum Systems Correlated with a Finite Bath: Nonequilibrium Dynamics and Thermodynamics

Describing open quantum systems far from equilibrium is challenging, in particular when the environment is mesoscopic, when it develops nonequilibrium features during the evolution, or when memory effects cannot be disregarded. Here we derive a master equation that explicitly accounts for system-bath correlations and includes, at a coarse-grained level, a dynamically evolving bath. It applies to a wide variety of environments; for instance, those that can be described by random matrix theory or the eigenstate thermalization hypothesis. We obtain a local detailed balance condition that does not forbid the emergence of stable negative temperature states in unison with the definition of temperature through the Boltzmann entropy. We benchmark the master equation against the exact evolution and observe very good agreement in a situation where the conventional Born-Markov-secular master equation breaks down. The present description of the dynamics is robust and it remains accurate even if some of the assumptions are relaxed. Even though our master equation describes a dynamically evolving bath not described by a Gibbs state, we provide a consistent nonequilibrium thermodynamic framework and derive the first and second law as well as the Clausius inequality. Our work paves the way for studying a variety of nanoscale quantum technologies, including engines, refrigerators, and heat pumps, beyond the conventionally used assumption of a static thermal bath.