Power-efficiency trade-off for finite-time quantum harmonic Otto heat engine via phase-space approach

TL;DR

This paper derives a universal power-efficiency trade-off relation for finite-time quantum harmonic Otto engines using phase-space methods, revealing how quantum coherence impacts engine performance and efficiency bounds.

Contribution

It introduces a novel phase-space approach to establish a universal trade-off relation for quantum engines operating in finite time, extending classical results to quantum regimes.

Findings

Power vanishes as efficiency approaches quantum bound

Maximum power occurs with minimal quantum coherence

Trade-off relation validated across various protocols

Abstract

Thermodynamic constraints impose a trade-off between power and efficiency in heat engines, preventing the simultaneous achievement of high power and high efficiency. For classical microscopic engines, explicit inequalities have been discovered, demonstrating the inherent inevitability of this power-efficiency trade-off. However, extensions of these results to quantum engines have so far been limited to cases of slow operation. In this study, we derive a power-efficiency trade-off relation for a paradigmatic quantum engine operating within a finite time, specifically the Otto cycle of a quantum harmonic oscillator. By utilizing a phase-space approach based on quasi-probability representations, we establish a universal trade-off relation applicable to arbitrary time-dependent protocols during the adiabatic processes. Our results reveal that the power of the quantum engine vanishes as the efficiency approaches the quantum mechanical efficiency bound, which is stricter than the Carnot bound. Furthermore, we identify the conditions under which the upper bound is attained, which indicate maximum power is achieved when the generation of quantum coherence is reduced, and the difference in time durations of the isochoric processes increases. These findings are validated through numerical calculations, which confirm their applicability across various types of protocols for heat engine cycles.