  The reduced state of a small system strongly coupled to a thermal bath may be
athermal and used as a small battery once disconnected. If the disconnecting
process is too slow, the coupling between the battery and the bath weakens, and
at some point, the battery will be in a thermal state that can not be used as a
battery. Thus, the unitarily extractable energy (a.k.a ergotropy) decreases
with the disconnection time. The work required to disconnect the battery also
depends on the disconnection time. We study the efficiency of this battery,
defined as the ratio between the ergotropy to the work cost of disconnecting
and connecting the battery back to the bath to close the cycle, as a function
of the disconnecting time in the Caldeira-Leggett model of a quantum battery.
We consider two scenarios. In the first scenario, we assume that the discharged
battery is uncorrelated to the bath at the connecting time and find that the
efficiency peaks at an optimal disconnecting time. In the second scenario, the
discharged battery is correlated to the bath, and find that the optimal
efficiency corresponds to an instantaneous disconnection. On top of these
results, we analyze various thermodynamic quantities for these Caldeira-Leggett
quantum batteries that allow us to express the first and second laws of
thermodynamics in the mentioned cycles in simple form despite the system-bath
initial correlations and strong coupling regime of the working device.
