  Starting from the observation that the reduced state of a system strongly
coupled to a bath is, in general, an athermal state, we introduce and study a
cyclic battery-charger quantum device that is in thermal equilibrium, or in a
ground state, during the charge storing stage. The cycle has four stages: the
equilibrium storage stage is interrupted by disconnecting the battery from the
charger, then work is extracted from the battery, and then the battery is
reconnected with the charger; finally, the system is brought back to
equilibrium. At no point during the cycle are the battery-charger correlations
artificially erased. We study the case where the battery and charger together
comprise a spin-1/2 Ising chain, and show that the main figures of merit - the
extracted energy and the thermodynamic efficiency - can be enhanced by
operating the cycle close to the quantum phase transition point. When the
battery is just a single spin, we find that the output work and efficiency show
a scaling behavior at criticality and derive the corresponding critical
exponents. Due to always present correlations between the battery and the
charger, operations that are equivalent from the perspective of the battery can
entail different energetic costs for switching the battery-charger coupling.
This happens only when the coupling term does not commute with the battery's
bare Hamiltonian, and we use this purely quantum leverage to further optimize
the performance of the device.
