Efficiency fluctuations of a heat engine with noise induced quantum coherences

We analyze the efficiency fluctuations of a coherent quantum heat engine coupled to a unimodal cavity using a standard full-counting statistics procedure. The engine's most likely efficiency obtained by computing the large-deviation function corresponds to the quantum efficiency obtained by defining a useful work obtainable from a steady-state fluctuation theorem. The most likely efficiency is independent of the noise induced coherences. The ratio between coherent and incoherent efficiency cumulants is found to be constant and independent of the stochastic efficiency, which we prove analytically. We also numerically demonstrate that treating the efficiency as a stochastic variable allows the enhancement of constancy only in the presence of coherences. At the engine's most likely efficiency, there is no suppression of the second efficiency cumulant leading to a robust constancy. We also report the existence of a lower bound on the second efficiency cumulant.