Entropy production and thermalization in the one-atom maser

Sending two-level atoms in a thermal state (one after the other) to a cavity with quantized monochromatic radiation, at equilibrium, was a thought experiment considered by Jaynes and Cummings in a paper introducing one of the most popular models in quantum optics.

They found that when the radiation frequency is not at resonance with the two-level energy splitting, the steady state of the system is thermal, with the temperatures of the two subsystems not equilibrated: apparently a violation of the principle of conservation of energy.

I was able to apply the entropy production formalism developed in my thesis to solve this puzzle. Under the specified conditions, the two subsystems behave as adiabatically insulated from each other, so there is no inconsistency.