Thermodynamics of a continuous quantum heat engine: Interplay between population and coherence

We present a detailed thermodynamic analysis of a three-level quantum heat engine coupled continuously to hot and cold reservoirs. The system is driven by an oscillating external field and is described by the Markovian quantum master equation. We use the general form of the dissipator which is consistent with thermodynamics. We calculate the heat, power, and efficiency of the system for the heat-engine operating regime and also examine the thermodynamic uncertainty relation. The efficiency of the system is strongly dependent on the structure of the dissipator, and the correlations between different levels can be an obstacle for ideal operation. In quantum systems, the heat flux is decomposed into the population and coherent parts. The coherent part is specific to quantum systems, and in contrast to the population part, it cannot be expressed by a simple series expansion in the linear-response regime. We discuss how the interplay between the population and coherent parts affects the performance of the heat engine.