Comment on "Carnot efficiency at divergent power output" (and additional discussion)

TL;DR

This paper critically examines claims that Carnot efficiency can be achieved at infinite power, clarifies misconceptions, and demonstrates that maximum efficiency occurs only at zero power in a specific quantum dot engine model.

Contribution

It refutes previous claims by analyzing the quantum dot engine and clarifies that Carnot efficiency is only attainable at zero power, correcting misconceptions about infinite power output.

Findings

Carnot efficiency is only achieved at zero output power.

The claimed divergence of power at Carnot efficiency is unsupported.

Infinite thermodynamical forces do not lead to finite power at Carnot efficiency.

Abstract

In a recent Letter [EPL, 118 (2017) 40003], Polettini and Esposito claimed that it is theoretically possible for a thermodynamic machine to achieve Carnot efficiency at divergent power output through the use of infinitely-fast processes. It appears however that this assertion is misleading as it is not supported by their derivations as demonstrated below. In this Comment, we first show that there is a confusion regarding the notion of optimal efficiency. We then analyze the quantum dot engine described in Ref. [EPL, 118 (2017) 40003] and demonstrate that Carnot efficiency is recovered only for vanishing output power. Moreover, a discussion on the use of infinite thermodynamical forces to reach Carnot efficiency is also presented in the appendix.