  We investigate the effects of noise-induced coherence on average current and
current fluctuations in a simple model of quantum absorption refrigerator with
degenerate energy levels. We describe and explain the differences and
similarities between the system behavior when it operates in the classical
regime, where the populations and coherences in the corresponding quantum
optical master equation decouple in a suitably chosen basis, and in the quantum
regime, where such a transformation does not exist. The differences between the
quantum and the classical case are observable only close to the maximum current
regime, where the system steady-state becomes non-unique. This allows us to
approximate the system dynamics by an analytical model based on a dichotomous
process, that explains the behavior of the average current both in the
classical and in the quantum case. Due to the non-uniqueness, the scaled
cumulant generating function for the current at the vicinity of the critical
point exhibits behavior reminiscent of the dynamical first-order phase
transition. Unless the system parameters are fine-tuned to a single point in
the parameter space, the corresponding current fluctuations are moderate in the
quantum case and large in the classical case.
