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We study the possibility of achieving the Carnot efficiency in a finite-powerunderdamped Brownian Carnot cycle. Recently, it was reported that the Carnotefficiency is achievable in a general class of finite-power Carnot cycles inthe vanishing limit of the relaxation times. Thus, it may be interesting toclarify how the efficiency and power depend on the relaxation times by using aspecific model. By evaluating the heat-leakage effect intrinsic in theunderdamped dynamics with the instantaneous adiabatic processes, we demonstratethat the compatibility of the Carnot efficiency and finite power is achieved inthe vanishing limit of the relaxation times in the small temperature-differenceregime. Furthermore, we show that this result is consistent with a trade-offrelation between power and efficiency by explicitly deriving the relation ofour cycle in terms of the relaxation times.

Compatibility of Carnot efficiency with finite power in an underdamped Brownian Carnot cycle in small temperature-difference regime