Comment on "Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries"

TL;DR

This paper critiques a previous study on quantum battery charging power, correcting the analysis and bounds related to fluctuations in extractable work, emphasizing the importance of accurate theoretical bounds.

Contribution

It identifies errors in prior work and provides corrected bounds on charging power, clarifying the relationship between fluctuations and power in quantum batteries.

Findings

Corrected the bound on charging power for quantum batteries.

Showed the previous analysis contained mistakes affecting the conclusions.

Revised the understanding of the link between work fluctuations and charging power.

Abstract

In an article by Garc\'ia-Pintos et al. [Rev. Lett. 125, 040601 (2020)] the connection between the charging power of a quantum battery and the fluctuations of a "free energy operator" whose expectation value characterizes the maximum extractable work of the battery is studied. The result of the closed-system analysis shows that for a general charging process the battery will have a nonzero charging power if and only if the state of the battery is not an eigenstate of the free energy operator. In this Comment, we point out a few mistakes in the analysis and obtain the correct bound on the charging power. Consequently, the result for closed-system dynamics is in general not correct.