Optimal operating protocol to achieve efficiency at maximum power of heat engines

Efficiency at maximum power has been investigated extensively, yet the practical control scheme to achieve it remains elusive. We fill this gap with a stepwise Carnot-like cycle, which consists of the discrete isothermal process (DIP) and adiabatic process. With DIP, we validate the widely adopted assumption of the C/t relation of the irreversible entropy generation S(ir) and show the explicit dependence of the coefficient C on the fluctuation of the speed of tuning energy levels as well as the microscopic coupling constants to the heat baths. Such a dependence allows us to control the irreversible entropy generation by choosing specific control schemes. We further demonstrate the achievable efficiency at maximum power and the corresponding control scheme with the simple two-level system. Our current work opens new avenues for an experimental test, which was not feasible due to the lack the of the practical control scheme in the previous low-dissipation model or its equivalents.