Consistency of Optimizing Finite-Time Carnot Engines with the Low-Dissipation Model in the Two-Level Atomic Heat Engine

The efficiency at the maximum power (EMP) for finite-time Carnot engines established with the low-dissipation model, relies significantly on the assumption of the inverse proportion scaling of the irreversible entropy generation $\Delta S^{ir}$ on the operation time $\tau$, i.e. $\Delta S^{ir}$ $\propto$ $1/ \tau$. The optimal operation time of the finite-time isothermal process for EMP has to be within the valid regime of the inverse proportion scaling. Yet, such consistency was not tested due to the unknown coefficient of the $1/ \tau$-scaling. In this paper, we reveal that the optimization of the finite-time two-level atomic Carnot engines with the low-dissipation model is consistent only in the regime of $η_C \ll 2(1 − \delta)/(1 + \delta)$, where $\eta_C$ is the Carnot efficiency, and δ is the compression ratio in energy level difference of the heat engine cycle. In the large-ηC regime, the operation time for EMP obtained with the low-dissipation model is not within the valid regime of the 1/τ-scaling, and the exact EMP of the engine is found to surpass the well-known bound $\eta_+ = \eta_C/(2 − \eta_C)$.

Communications in Theoretical Physics