Irreversible quantum Carnot cycle and its comparison with quantum Otto cycle

A generic working substance that does not satisfy the scale-invariance property is investigated for the irreversible quantum Carnot heat engine cycle. Two construction scenarios of the cycle are compared: one optimizes the irreversible cycle, while the other maintains fixed parameters by establishing the scale-invariance within the possible scalable energy limit. It is found that the irreversible Carnot cycle efficiency always falls below the classical limit, depending on reservoir and system specifics. In contrast, in certain parameter regimes, the irreversible cycle can extract more work than the reversible cycle. Additionally, the optimized scenario enables efficient work extraction in regimes where the reversible cycle fails to function as a heat engine. The study also extends to a quantum Otto cycle with the same working medium, comparing its performance against that of the irreversible Carnot cycle. Parameter regimes where the Otto cycle is superior to the Carnot cycle are explored.