Efficiency at maximum power output of quantum heat engines under finite-time operation

TL;DR

This paper analyzes the efficiency at maximum power of finite-time quantum heat engines, deriving bounds and conditions under which classical efficiencies like Carnot and Curzon-Ahlborn are recovered.

Contribution

It provides bounds on the efficiency at maximum power for quantum Carnot engines considering nonadiabatic dissipation and finite-time effects.

Findings

Efficiency bounds depend on Carnot efficiency, with upper bound $rac{ ext{η}_C}{2- ext{η}_C}$.

Symmetric dissipation yields Curzon-Ahlborn efficiency under specific time allocation.

Reversible limit recovers Carnot efficiency at maximum power.

Abstract

We study the efficiency at maximum power, $\eta_m$, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures $T_h$ and $T_c$, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), $\eta_m$ becomes identical to Carnot efficiency $\eta_{_C}=1-\frac{T_c}{T_h}$. For QCE cycles in which nonadiabatic dissipation and time spent on two adiabats are included, the efficiency $\eta_m$ at maximum power output is bounded from above by $\frac{\eta_{_C}}{2-\eta_{_C}}$ and from below by $\frac{\eta_{_C}}2$. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency $\eta_{_{CA}}=1-\sqrt{\frac{T_c}{T_h}}$ is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.