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)/2 and eta(C)/(2 - eta(C)), eta(C)/2 and eta(C), 0 and eta(C)/(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 (2012) 40001] although the dissipative engines and the irreversible ones are inequivalent to each other.