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 Δ S (ir) on the operation time τ , i.e. Δ S (ir) ∝ 1/ 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, 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 ≪ 2(1 − δ )/(1 + δ ), where η C is the Carnot efficiency, and δ is the compression ratio in energy level difference of the heat engine cycle. 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 of the engine is found to surpass the well-known bound η + = η C /(2 − η C ).