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We investigate the performance of an underdamped stochastic heat engine for atime-dependent harmonic oscillator. We analytically determine the optimalprotocol that maximizes the efficiency at fixed power. The maximum efficiencyreduces to the Curzon-Ahlborn formula at maximum power and the Carnot formulaat zero power. We further establish that the efficiency at maximum power isuniversally given by the Curzon-Ahlborn efficiency in the weakly damped regime.Finally, we show that even small deviations from operation at maximum power mayresult in a significantly increased efficiency.

Underdamped stochastic heat engine at maximum efficiency