Nonequilibrium dynamics with finite-time repeated interactions

In the thermodynamics of elementary quantum systems, repeated interactions with environmental probes can be used as a template to model relaxation in various reservoir types. We formulate a coarse-grained master equation that spans arbitrary interaction strengths and times, extending beyond previous short-time treatments with just identical probes. Using this, we show that instead of thermalization, repeated interactions in a thermal environment generally lead to out-of-equilibrium states including population inversion. In composite systems, local repeated interactions are neither compatible with the resource-theoretical notion of thermal operations nor with the Born-Markov secular treatment of thermalization.