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

1 page, submitted to the journal the 23rd of December 2020