Exact bound of power-efficiency trade-off in finite-time thermodynamic cycles

Power and efficiency are fundamental criteria for evaluating the performance of thermodynamic cycles. However, it is generally impossible to maximize both simultaneously. In particular, achieving maximum efficiency inevitably leads to vanishing power as the cycle duration approaches infinity. A quantitative characterization of this trade-off yields significant theoretical and practical implications. In this letter, we analytically derive an exact bound constraining power and efficiency in low-dissipation finite-time heat engines. This bound specifies the maximum power attainable at any prescribed efficiency, thereby providing a benchmarking for evaluating the performance of heat engines.