Physical Review Letters

García-Pintos, Hamma, and del Campo Reply:

Luis Pedro García-Pintos, Alioscia Hamma, Adolfo del Campo

Published Jul 9, 2021• 4 citations

Abstract

We acknowledge that a derivation reported in Phys. Rev. Lett. 125, 040601 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.040601 is incorrect as pointed out by Cusumano and Rudnicki. We respond by giving a correct proof of the claim "fluctuations in the free energy operator upper bound the charging power of a quantum battery" that we made in the Letter.

DOI: 10.1103/physrevlett.127.028902

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Physical Review Letters

García-Pintos, Hamma, and del Campo Reply:

Luis Pedro García-Pintos, Alioscia Hamma, Adolfo del Campo

Published Jul 9, 2021• 4 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.127.028902

Related papers

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

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In an article by García-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.In an article by García-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.

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In the abstract of [Phys. Rev. Lett. 125, 040601 (2020)] one can read that ``[ $\dots{}$ ] to have a nonzero rate of change of the extractable work, the state ${\ensuremath{\rho}}_{\mathcal{W}}$ of the battery cannot be an eigenstate of a `free energy operator,' defined by $\mathcal{F}\ensuremath{\equiv}{H}_{\mathcal{W}}+{\ensuremath{\beta}}^{\ensuremath{-}1}\mathrm{log}({\ensuremath{\rho}}_{\mathcal{W}})$, where ${H}_{\mathcal{W}}$ is the Hamiltonian of the battery and $\ensuremath{\beta}$ is the inverse temperature [ $\dots{}$ ].'' Contrarily to what is presented below Eq. (17) of the Letter, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.In the abstract of [Phys. Rev. Lett. 125, 040601 (2020)] one can read that ``[$\dots{}$] to have a nonzero rate of change of the extractable work, the state ${\ensuremath{\rho}}_{\mathcal{W}}$ of the battery cannot be an eigenstate of a `free energy operator,' defined by $\mathcal{F}\ensuremath{\equiv}{H}_{\mathcal{W}}+{\ensuremath{\beta}}^{\ensuremath{-}1}\mathrm{log}({\ensuremath{\rho}}_{\mathcal{W}})$, where ${H}_{\mathcal{W}}$ is the Hamiltonian of the battery and $\ensuremath{\beta}$ is the inverse temperature [$\dots{}$].'' Contrarily to what is presented below Eq. (17) of the Letter, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.

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Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries

Luis Pedro García-Pintos, Alioscia Hamma, Adolfo del Campo

We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a nonzero rate of change of the extractable work, the state ${\ensuremath{\rho}}_{\mathcal{W}}$ of the battery cannot be an eigenstate of a ``free energy operator,'' defined by $\mathcal{F}\ensuremath{\equiv}{H}_{\mathcal{W}}+{\ensuremath{\beta}}^{\ensuremath{-}1}\mathrm{log}({\ensuremath{\rho}}_{\mathcal{W}})$, where ${H}_{\mathcal{W}}$ is the Hamiltonian of the battery and $\ensuremath{\beta}$ is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a nonzero rate of change of the extractable work, the state ${\ensuremath{\rho}}_{\mathcal{W}}$ of the battery cannot be an eigenstate of a ``free energy operator,'' defined by $\mathcal{F}\ensuremath{\equiv}{H}_{\mathcal{W}}+{\ensuremath{\beta}}^{\ensuremath{-}1}\mathrm{log}({\ensuremath{\rho}}_{\mathcal{W}})$, where ${H}_{\mathcal{W}}$ is the Hamiltonian of the battery and $\ensuremath{\beta}$ is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.

arXiv:1909.03558Physical Review LettersJul 22, 2020133 citations

In the abstract of [Phys. Rev. Lett. 125, 040601 (2020)] one can read that ``[

\dots{}

] to have a nonzero rate of change of the extractable work, the state ${\ensuremath{\rho}}_{\mathcal{W}}$ of the battery cannot be an eigenstate of a `free energy operator,' defined by $\mathcal{F}\ensuremath{\equiv}{H}_{\mathcal{W}}+{\ensuremath{\beta}}^{\ensuremath{-}1}\mathrm{log}({\ensuremath{\rho}}_{\mathcal{W}})$, where

{H}_{\mathcal{W}}

is the Hamiltonian of the battery and $\ensuremath{\beta}$ is the inverse temperature [

\dots{}

].'' Contrarily to what is presented below Eq. (17) of the Letter, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.

{H}_{\mathcal{W}}

is the Hamiltonian of the battery and $\ensuremath{\beta}$ is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.