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.