Consistency of optimizing finite-time Carnot engines with the low-dissipation model in the two-level atomic heat engine

Yu-Han Ma,C P Sun,Hui Dong

Figure 4. Efficiency at the maximum power ηMP (orange solid line) of the heat engine as the function of the Carnot efficiency ηC for different final energy spacing of the two level system(a) ${\omega }_{{\rm{h}}}^{{\rm{f}}}=0.6$ and (b) ${\omega }_{{\rm{h}}}^{{\rm{f}}}=0.9$. The black dashed line (black dash-dotted line) represents the upper bound η+ (lower bound η−) of EMP obtained with the low-dissipation model [equation (4)], and the Carnot efficiency ηC is plotted with the black dotted line. The gray area represents the low-dissipation regime predicted by equation (10). (c) Optimal operation time ${\tau }_{{\rm{h}}}^{* }$ at the maximum power as the function of ηC. The blue solid curve is obtained with ${\omega }_{{\rm{h}}}^{{\rm{f}}}=0.6$ (δ = 0.6) while the red dash-dotted curve is obtained with ${\omega }_{{\rm{h}}}^{{\rm{f}}}=0.9$ (δ = 0.9). The other parameters in this figure are chosen as ${\omega }_{{\rm{h}}}^{{\rm{i}}}=1$, γh = 1, and Th = 10. The relaxation time is ${t}_{{\rm{r}}}={\omega }_{{\rm{h}}}^{{\rm{i}}}/\left(2{\gamma }_{{\rm{h}}}{T}_{{\rm{h}}}\right)=0.05$.