Stochastic Scovil--Schulz-DuBois machine and its three types of cycles

Three types of cycles are identified in the quantum jump trajectories of the Scovil--Schulz-DuBois (SSDB) machine: an R-cycle as refrigeration, an H-cycle as a heat engine, and an N-cycle in which the machine is neutral. The statistics of these cycles are investigated via a semi-Markov process method. We find that in the large time limit, whether the machine operates as a heat engine or refrigerator depends on the ratio between the numbers of R-cycles and H-cycles per unit time. Further increasing the hot bath temperature above a certain threshold does not increase the machine's power output. The cause is that, in this situation, the N-cycle has a greater probability than the H-cycle and R-cycle. Although the SSDB machine operates by randomly switching between these three cycles, at the level of a single quantum jump trajectory, its heat engine efficiency and the refrigerator's coefficient of performance remain constant.