  How much work can be extracted from a heat bath using a thermal machine? The
study of this question has a very long tradition in statistical physics in the
weak-coupling limit, applied to macroscopic systems. However, the assumption
that thermal heat baths remain uncorrelated with physical systems at hand is
less reasonable on the nano-scale and in the quantum setting. In this work, we
establish a framework of work extraction in the presence of quantum
correlations. We show in a mathematically rigorous and quantitative fashion
that quantum correlations and entanglement emerge as a limitation to work
extraction compared to what would be allowed by the second law of
thermodynamics. At the heart of the approach are operations that capture
naturally non-equilibrium dynamics encountered when putting physical systems
into contact with each other. We discuss various limits that relate to known
results and put our work into context of approaches to finite-time quantum
thermodynamics.
