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We investigate quantum Otto engine and refrigeration cycles of atime-dependent harmonic oscillator operating under the conditions of maximum$\Omega$-function, a trade-off objective function which represents a compromisebetween energy benefits and losses for a specific job, for both adiabatic andnonadiabatic (sudden) frequency modulations. We derive analytical expressionsfor the efficiency and coefficient of performance of the Otto cycle. For thecase of adiabatic driving, we point out that in the low-temperature regime, theharmonic Otto engine (refrigerator) can be mapped to Feynman's ratchet and pawlmodel which is a steady state classical heat engine. For the sudden switch offrequencies, we obtain loop-like behavior of the efficiency-work curve, whichis characteristic of irreversible heat engines. Finally, we discuss thebehavior of cooling power at maximum $\Omega$-function and indicate the optimaloperational point of the refrigerator.

Unified trade-off optimization of quantum harmonic Otto engine and refrigerator