Time-resolved Stochastic Dynamics of Quantum Thermal Machines

Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum jumps, each representing the exchange of finite quanta with the environment. In this work, we present a framework that resolves the dynamics of quantum thermal machines into cycles that are classified as engine-like, cooling-like, or idle. We explore the statistics of each cycle type and its duration, enabling us to determine both the fraction of cycles useful for thermodynamic tasks and the average waiting time between cycles of the same type. Our framework presents a novel approach in characterizing thermal machines, with significant relevance to modern experiments, such as mesoscopic transport using quantum dots.