Geometric Heat Engines Featuring Power that Grows with Efficiency

TL;DR

This paper introduces a geometric framework to analyze and optimize heat engine power and efficiency as functions of cycle time, demonstrating protocols that maximize both at fast driving limits and proving the unattainability of Carnot efficiency at non-zero power.

Contribution

It develops a novel geometric approach to describe and optimize heat engine performance, enabling design of protocols that maximize power and efficiency simultaneously.

Findings

Protocols achieving maximal power and efficiency at fast driving limits.

Proof that Carnot efficiency cannot be reached at non-zero power.

A general geometric description applicable to key heat engine models.

Abstract

Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this manuscript, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method we also prove that no protocol can exactly attain the Carnot efficiency at non-zero power.