Bounds of Efficiency at Maximum Power for Normal-, Sub- and Super-Dissipative Carnot-Like Heat Engines

The Carnot-like heat engines are classified into three types (normal-, sub- and super-dissipative) according to relations between the minimum irreversible entropy production in the “isothermal” processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between ${\eta }_C\mathrm{/}2$ and ${\eta }_C\mathrm{/}(2-{\eta }_C)$, ${\eta }_C\mathrm{/}2$ and ${\eta }_C$, 0 and ${\eta }_C\mathrm{/}(2-{\eta }_C)$, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98, 40001 (2012)] although the dissipative engines and the irreversible ones are inequivalent to each other.