Extraction of classical ergotropy

Finding the time dependent perturbation that extracts the maximal amount of energy (a.k.a. ergotropy) from a thermally isolated quantum system is a central, solved, problem in quantum thermodynamics. Notably, the same problem has been long studied for classical systems as well, e.g., in the field of plasma physics, but a general solution is still missing there. By building on the analogy with the quantum solution, we provide the classical ergotropy extraction driving: it consists of an instantaneous quench followed by an adiabatic return. The solution is valid under the ergodic hypothesis and we also show that for quantum systems that are classically ergodic the classical expression of ergotropy emerges as the semiclassical limit of the quantum one. The presented results open new ways for practical energy recovery in the classical regime and for understanding the genuine quantum features of quantum ergotropy.