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For illustrative purposes we consider the problem of the plasmon linewidth in a homogeneous electron gas (jellium).In the abstract of [Phys. Rev. Lett. 125, 040601 (202PRLTAO0031-900710.1103/PhysRevLett.125.040601] one can read that "[…] to have a nonzero rate of change of the extractable work, the state ρ_W of the battery cannot be an eigenstate of a 'free energy operator,' defined by F≡H_W+β^-1log(ρ_W), where H_W is the Hamiltonian of the battery and β is the inverse temperature […]." Contrarily to what is presented below Eq. (17) of
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