Positivity of entropy production for the three-level maser

Entropy production is a key concept of thermodynamics and allows one to analyze the operation of engines. For the Scovil-Schulz-DuBois heat engine, the archetypal three-level thermal maser coupled to thermal baths, it was argued that the common definition of heat flow may provide negative entropy production for certain parameters [Boukobza and Tannor, Phys. Rev. Lett. 98, 240601 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.240601]. Here, we show that this can be cured if corrections for detuning are properly applied to the energies used for the bath transitions. This method can be used more generally for the thermodynamical analysis of optical transitions where the modes of the light field are detuned from the transition energy.