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

Abstract

We study the efficiency at maximum power, $η_m$, 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), $η_m$ becomes identical to Carnot efficiency $η_{_C}=1-\frac{T_c}{T_h}$. For QCE cycles in which nonadiabatic dissipation and time spent on two adiabats are included, the efficiency $η_m$ at maximum power output is bounded from above by $\frac{η_{_C}}{2-η_{_C}}$ and from below by $\frac{η_{_C}}2$. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency $η_{_{CA}}=1-\sqrt{\frac{T_c}{T_h}}$ is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.