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

TL;DR

This paper analyzes quantum harmonic Otto engines and refrigerators operating under a trade-off criterion, deriving analytical expressions for efficiency and performance, and exploring their behavior under adiabatic and sudden frequency modulations.

Contribution

It introduces a unified framework for optimizing quantum Otto cycles using the $ ext{Omega}$-function, providing analytical results and insights into both adiabatic and nonadiabatic regimes.

Findings

In the adiabatic regime, the engine maps to Feynman's ratchet model at low temperatures.

Sudden frequency changes produce loop-like efficiency-work behavior indicating irreversibility.

Optimal cooling power and operational points are identified for the refrigerator.

Abstract

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