Maximum Efficiency of Low-Dissipation Heat Engines at Arbitrary Power

TL;DR

This paper analyzes the maximum achievable efficiency of low-dissipation heat engines at any given power level, revealing universal bounds and scaling laws that extend previous results on efficiency at maximum power.

Contribution

It introduces universal bounds on efficiency at arbitrary power for low-dissipation engines and generalizes earlier bounds on efficiency at maximum power.

Findings

Efficiency gain scales as square root of power loss near maximum power

Engines can operate at higher efficiency close to maximum power

Universal bounds on efficiency at given power are derived and supported by numerical evidence

Abstract

We investigate maximum efficiency at a given power for low-dissipation heat engines. Close to maximum power, the maximum gain in efficiency scales as a square root of relative loss in power and this scaling is universal for a broad class of systems. For the low-dissipation engines, we calculate the maximum gain in efficiency for an arbitrary fixed power. We show that the engines working close to maximum power can operate at considerably larger efficiency compared to the efficiency at maximum power. Furthermore, we introduce universal bounds on maximum efficiency at a given power for low-dissipation heat engines. These bounds represent direct generalization of the bounds on efficiency at maximum power obtained by Esposito et al. Phys. Rev. Lett. 105, 150603 (2010). We derive the bounds analytically in the regime close to maximum power and for small power values. For the intermediate regime we present strong numerical evidence for the validity of the bounds.