Universal bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis

We show that the maximum extractable work (ergotropy) from a quantum many-body system is constrained by local athermality of an initial state and local entropy decrease brought about by quantum operations. The obtained universal bound on ergotropy implies that the eigenstate thermalization hypothesis prohibits work extraction from energy eigenstates by means of finite-time unitary operations. This no-go property implies that Planck's principle, a form of the second law of thermodynamics, holds even for pure quantum states. Our result bridges two independently studied concepts of quantum thermodynamics, the second law and thermalization, via intrasystem correlations in many-body systems as a resource for work extraction.