A microscopic theory of Curzon-Ahlborn heat engine

TL;DR

This paper develops a microscopic stochastic differential equation framework for the Curzon-Ahlborn heat engine, providing a solid theoretical foundation and analytical expressions for power and efficiency statistics, advancing understanding of microscopic finite-time heat engines.

Contribution

It introduces a microscopic theory of the CA engine using stochastic differential equations, clarifying assumptions and deriving analytical power and efficiency expressions.

Findings

Provides microscopic interpretation of CA assumptions

Derives analytical power and efficiency statistics

Enhances understanding of microscopic heat engine fluctuations

Abstract

Abstract The Curzon-Ahlborn (CA) efficiency, as the efficiency at the maximum power (EMP) of the endoreversible Carnot engine, has a significant impact on finite-time thermodynamics. However, the CA engine model is based on many assumptions. In the past few decades, although a lot of efforts have been made, a microscopic theory of the CA engine is still lacking. By adopting the method of the stochastic differential equation of energy, we formulate a microscopic theory of the CA engine realized with an underdamped Brownian particle in a class of non-harmonic potentials. This theory gives microscopic interpretation of all assumptions made by Curzon and Ahlborn, and thus puts the results about CA engine on a solid foundation. Also, based on this theory, we obtain analytical expressions of the power and the efficiency statistics for the Brownian CA engine. Our research brings new perspectives to experimental studies of finite-time microscopic heat engines featured with fluctuations.