  Thermodynamics of a three-level maser was studied in the pioneering work of
Scovil and Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)]. In this work we
consider the same three-level model, but treat both the matter and light
quantum mechanically. Specifically, we analyze an extended (three-level)
dissipative Jaynes-Cummings model (ED-JCM) within the framework of a quantum
heat engine, using novel formulas for heat flux and power in bipartite systems
introduced in our previous work [E. Boukobza and D. J. Tannor, PRA (in press)].
Amplification of the selected cavity mode occurs even in this simple model, as
seen by a positive steady state power. However, initial field coherence is
lost, as seen by the decaying off-diagonal field density matrix elements, and
by the Husimi-Kano Q function. We show that after an initial transient time the
field's entropy rises linearly during the operation of the engine, which we
attribute to the dissipative nature of the evolution and not to matter-field
entanglement. We show that the second law of thermodynamics is satisfied in two
formulations (Clausius, Carnot) and that the efficiency of the ED-JCM heat
engine agrees with that defined intuitively by Scovil and Schulz-DuBois.
Finally, we compare the steady state heat flux and power of the fully quantum
model with the semiclassical counterpart of the ED-JCM, and derive the engine
efficiency formula of Scovil and Schulz-DuBois analytically from fundamental
thermodynamic fluxes.
