Efficiency at maximum power of a quantum Otto engine: Both within finite-time and irreversible thermodynamics

TL;DR

This paper analyzes the efficiency at maximum power of a quantum Otto engine with spin or harmonic systems, revealing universal bounds and connections to irreversible thermodynamics and the Curzon-Ahlborn efficiency.

Contribution

It derives a universal upper bound for the efficiency at maximum power of quantum Otto engines using different quantum systems, linking it to irreversible thermodynamics.

Findings

Efficiency at maximum power is bounded by a universal expression for different quantum systems.

The Curzon-Ahlborn efficiency serves as an upper bound in the linear-response regime.

The study connects quantum engine performance with classical thermodynamic bounds.

Abstract

We consider the efficiency at maximum power of a quantum Otto engine, which uses a spin or a harmonic system as its working substance and works between two heat reservoirs at constant temperatures $T_h$ and $T_c$ $ (<T_h)$. Although the spin-$1/2$ system behaves quite differently from the harmonic system in that they obey two typical quantum statistics, the efficiencies at maximum power based on these two different kinds of quantum systems are bounded from the upper side by the same expression of the efficiency at maximum power: $\eta_{mp}\leq\eta_+\equiv \eta_C^2/[\eta_C-(1-\eta_C)\ln(1-\eta_C)]$, with $\eta_C=1-T_c/T_h$ the Carnot efficiency, which displays the same universality of the CA efficiency $\eta_{CA}=1-\sqrt{1-\eta_C}$ at small relative temperature difference. Within context of irreversible thermodynamics, we calculate the Onsager coefficients and, we show that the value of $\eta_{CA}$ is indeed the upper bound of EMP for the Otto engines working in the linear-response regime.