Entropy production and thermalization in the one-atom maser

In the configuration in which two-level atoms with an initial thermal distribution of their states are sent in succession to a cavity sustaining a single mode of electromagnetic radiation, one atom leaving the cavity as the next one enters it (as in the one-atom maser), Jaynes and Cummings showed that the steady state of the field, when many atoms have traversed the cavity, is thermal with a temperature different than that of the atoms in the off-resonant situation. Having an interaction between two subsystems which maintains them at different temperatures was then understood as leading to an apparent violation of energy conservation. Here we show, by calculating the quantum entropy production in the system, that this difference of temperatures is consistent with having the subsystems adiabatically insulated from each other as the steady state is approached. At resonance the insulation is removed and equilibration of the temperatures is achieved.