Coupled autonomous thermal machines and efficiency at maximum power

TL;DR

This paper presents a unified theoretical framework for understanding the efficiency at maximum power of coupled autonomous thermal machines with three heat reservoirs, revealing universal properties and new coefficients near equilibrium.

Contribution

It introduces a global linear-irreversible model that unifies various expressions for EMP and predicts a universal second order coefficient for broken time reversal symmetry.

Findings

Efficiency at maximum power can be expressed using Carnot efficiency with algebraic mean reservoir temperatures.

Universal properties of EMP near equilibrium are explained via symmetric algebraic means.

A new universal second order coefficient of 6/49 is predicted for systems with broken time reversal symmetry.

Abstract

We show that coupled autonomous thermal machines, in the presence of three heat reservoirs and following a global linear-irreversible description, provide a unified framework to accommodate the variety of expressions for the efficiency at maximum power (EMP). The efficiency is expressible in terms of the Carnot efficiency of the global set up if the intermediate reservoir temperature is an algebraic mean of the hot and cold temperatures. We give an explanation of the universal properties of EMP near equilibrium in terms of the properties of symmetric algebraic means. For the case of broken time reversal symmetry, a universal second order coefficient of 6/49 is predicted in the series expansion of EMP, analogous to the 1/8 coefficient in the time-reversal symmetric case.