Charging assisted by thermalization

Abstract

A system in thermal equilibrium with a bath will generally be in an athermal state, if the system-bath coupling is strong. In some cases, it will be possible to extract work from that athermal state, after disconnecting the system from the bath. We use this observation to devise a battery charging and storing unit, simply consisting of a system, acting as the battery, and a bath. The charging cycle---connect, let thermalize, disconnect, extract work---requires very little external control and the charged state of the battery, being a part of global thermal equilibrium, can be maintained indefinitely and for free. The efficiency, defined as the ratio of the extractable work stored in the battery and the total work spent on connecting and disconnecting, is always $\leq 1$, which is a manifestation of the second law of thermodynamics. Moreover, coupling, being a resource for the device, is also a source of dissipation: the entropy production per charging cycle is always significant, strongly limiting the efficiency in all coupling strength regimes. We show that our general results also hold for generic microcanonical baths. We illustrate our theory on the Caldeira-Leggett model with a harmonic oscillator (the battery) coupled to a harmonic bath, for which we derive general asymptotic formulas in both weak and ultrastrong coupling regimes, for arbitrary Ohmic spectral densities. We show that the efficiency can be increased by connecting several copies of the battery to the bath. Finally, as a side result, we derive a general formula for Gaussian ergotropy, that is, the maximal work extractable by Gaussian unitary operations from Gaussian states of multipartite continuous-variable systems.