Optimizing thermodynamic cycles with two finite-sized reservoirs

We study the nonequilibrium thermodynamics of a heat engine operating between two finite-sized reservoirs with well-defined temperatures. Within the linear response regime, it is found that the uniform temperature of the two reservoirs at final time tau is bounded from below by the entropy production sigma(min )proportional to 1/tau. We discover a general power-efficiency tradeoff depending on the ratio of heat capacities (gamma) of the reservoirs for the engine, and a universal efficiency at maximum average power of the engine for arbitrary gamma is obtained. For practical purposes, the operation protocol of an ideal gas heat engine to achieve the optimal performance associated with sigma(min) is demonstrated. Our findings can be used to develop a general optimization scenario for thermodynamic cycles with finite-sized reservoirs in real-world circumstances.