Efficiency at and near Maximum Power of Low-Dissipation Heat Engines

TL;DR

This paper introduces a universal approach to optimize the efficiency-power trade-off in low-dissipation heat engines, revealing bounds and diseconomies of engines at maximum power, with demonstrations on theoretical measures and a diffusion-based model.

Contribution

It presents a universal optimization framework for trade-offs between power and efficiency in low-dissipation Carnot cycles, independent of detailed dynamics.

Findings

Universal bounds on efficiency at maximum trade-off.

Diseconomy of engines operating at maximum power.

Validation on a diffusion-based heat engine model.

Abstract

A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum value can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs. The result is demonstrated on two specific trade-off measures. The first one is designed for finding optimal efficiency for a given output power and clearly reveals diseconomy of engines working at maximum power. As the second example we derive universal lower and upper bounds on the efficiency at maximum trade-off given by the product of power and efficiency. The results are illustrated on a model of a diffusion-based heat engine. Such engines operate in the low-dissipation regime given that the used driving minimizes the work dissipated during the isothermal branches. The peculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed.