  Thermodynamics of quantum systems out-of-equilibrium is very important for
the progress of quantum technologies, however, the effects of many body
interactions and their interplay with temperature, different drives and
dynamical regimes is still largely unknown. Here we present a systematic study
of these interplays: we consider a variety of interaction (from non-interacting
to strongly correlated) and dynamical (from sudden quench to quasi-adiabatic)
regimes, and draw some general conclusions in relation to work extraction and
entropy production. As treatment of many-body interacting systems is highly
challenging, we introduce a simple approximation which includes, for the
average quantum work, many-body interactions only via the initial state, while
the dynamics is fully non-interacting. We demonstrate that this simple
approximation is surprisingly good for estimating both the average quantum work
and the related entropy variation, even when many-body correlations are
significant.
