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

TL;DR

This paper investigates whether Carnot efficiency can be achieved at finite power in an underdamped Brownian cycle, showing that in the small temperature difference regime, this is possible as relaxation times approach zero, consistent with power-efficiency trade-offs.

Contribution

It demonstrates the compatibility of Carnot efficiency with finite power in an underdamped Brownian cycle by analyzing relaxation times and heat leakage effects.

Findings

Carnot efficiency is achievable at finite power in the vanishing relaxation time limit.

The result holds in the small temperature-difference regime.

The study confirms the power-efficiency trade-off relation in this context.

Abstract

We study the possibility of achieving the Carnot efficiency in a finite-power underdamped Brownian Carnot cycle. Recently, it was reported that the Carnot efficiency is achievable in a general class of finite-power Carnot cycles in the vanishing limit of the relaxation times. Thus, it may be interesting to clarify how the efficiency and power depend on the relaxation times by using a specific model. By evaluating the heat-leakage effect intrinsic in the underdamped dynamics with the instantaneous adiabatic processes, we demonstrate that the compatibility of the Carnot efficiency and finite power is achieved in the vanishing limit of the relaxation times in the small temperature-difference regime. Furthermore, we show that this result is consistent with a trade-off relation between power and efficiency by explicitly deriving the relation of our cycle in terms of the relaxation times.