  We examine when it is possible to locally extract energy from a bipartite
quantum system in the presence of strong coupling and entanglement, a task
which is expected to be restricted by entanglement in the low-energy
eigenstates. We fully characterize this distinct notion of "passivity" by
finding necessary and sufficient conditions for such extraction to be
impossible, using techniques from semidefinite programming. This is the first
time in which such techniques are used in the context of energy extraction,
which opens a way of exploring further kinds of passivity in quantum
thermodynamics. We also significantly strengthen a previous result of Frey et
al., by showing a physically relevant quantitative bound on the threshold
temperature at which this passivity appears. Furthermore, we show how this
no-go result also holds for thermal states in the thermodynamic limit, provided
that the spatial correlations decay sufficiently fast, and we give numerical
examples.
