Onsager coefficients of a Brownian Carnot cycle

TL;DR

This paper analyzes a Brownian Carnot cycle using linear irreversible thermodynamics, deriving Onsager coefficients that depend on protocol shape and satisfy tight-coupling, shedding light on efficiency limits of finite-time heat engines.

Contribution

It provides a general method to calculate Onsager coefficients for arbitrary protocols in a Brownian Carnot cycle, revealing their protocol dependence and tight-coupling property.

Findings

Onsager coefficients depend on the protocol shape.

Coefficients satisfy the tight-coupling condition.

Results may explain the ubiquity of Curzon-Ahlborn efficiency.

Abstract

We study a Brownian Carnot cycle introduced by T. Schmiedl and U. Seifert [Europhys. Lett. \textbf{81}, 20003 (2008)] from a viewpoint of the linear irreversible thermodynamics. By considering the entropy production rate of this cycle, we can determine thermodynamic forces and fluxes of the cycle and calculate the Onsager coefficients for general protocols, that is, arbitrary schedules to change the potential confining the Brownian particle. We show that these Onsager coefficients contain the information of the protocol shape and they satisfy the tight-coupling condition irrespective of whatever protocol shape we choose. These properties may give an explanation why the Curzon-Ahlborn efficiency often appears in the finite-time heat engines.