Self-consistency of optimizing finite-time Carnot engines with the low-dissipation model

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 ΔS^\(ir\) on the operation time τ, i.e., ΔS^\(ir\)propto1/τ. 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/τ-scaling. In this paper, using a two-level atomic heat engine as an illustration, we reveal that the optimization of the finite-time Carnot engines with the low-dissipation model is self-consistent only in the regime of η_Cll1, where η_C is the Carnot efficiency. In the large-η_C 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 is found to surpass the well-known bound η₊=η_C/\(2-η_C\)