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

TL;DR

This paper critiques a previous claim about quantum batteries, showing that the conclusion about extractable work fluctuations does not hold under nonunitary dynamics, thus clarifying the conditions for work change in quantum systems.

Contribution

It provides a counterexample to the previous claim, demonstrating that the earlier conclusion is invalid when the battery undergoes nonunitary evolution.

Findings

The previous claim about zero work change does not hold under nonunitary dynamics.

Nonunitary processes can enable fluctuations in extractable work.

The paper clarifies the conditions affecting work fluctuations in quantum batteries.

Abstract

In the abstract of~[Phys. Rev. Lett. {\bf 125}, 040601 (2020)] one can read that: [...]{\it to have a nonzero rate of change of the extractable work, the state $\rho_\mathcal{W}$ of the battery cannot be an eigenstate of a "free energy operator", defined by $\mathcal{F}=H_\mathcal{W}+\beta^{-1}\log \rho_\mathcal{W}$, where $H_\mathcal{W}$ is the Hamiltonian of the battery and $\beta$ is the inverse temperature} [...]. Contrarily to what is presented below Eq.~(17) of the paper, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.