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

TL;DR

This paper proposes a practical control scheme using a stepwise Carnot-like cycle to optimize the efficiency at maximum power of heat engines, validated through a two-level system model and highlighting the influence of control parameters.

Contribution

It introduces a stepwise Carnot-like cycle with explicit control of irreversible entropy generation, enabling practical achievement of maximum power efficiency in heat engines.

Findings

Validated the /t relation of irreversible entropy generation.

Showed dependence of  on energy level fluctuation and coupling constants.

Demonstrated control scheme effectiveness with a two-level system.

Abstract

The efficiency at maximum power has been investigated extensively, yet the practical control scheme to achieve it remains elusive. We fill such gap with a stepwise Carnot-like cycle, which consists the discrete isothermal process (DIP) and adiabatic process. With DIP, we validate the widely adopted assumption of \mathscr{C}/t relation of the irreversible entropy generation S^{(\mathrm{ir})}, and show the explicit dependence of the coefficient \mathscr{C} on the fluctuation of the speed of tuning energy levels as well as the microscopic coupling constants to the heat baths. Such dependence allows 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 the 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.