Operational Constraints in Quantum Otto Engines: Energy-Gap Modulation and Majorization

The performance of a quantum Otto engine is analyzed with regard to the constraints on the modulation of energy gaps relative to the changes in probability distributions at the two given heat reservoirs. We performed a detailed analysis with a generic three-level system (3LS), which serves as a non-trivial working medium with two energy gaps. A three-level Otto engine becomes feasible if at least one energy gap shrinks during the first quantum adiabatic stage. The operating regimes are derived for each allowed energy gap modulation, and majorization is observed to play a crucial role in determining the engine operation. This results in an enhanced Otto efficiency when the probability distributions fulfill the majorization condition. Finally, we show that our formalism applies to a swap engine based on a working medium composed of two 3LSs.