  Presence of correlations among the constituent quantum systems has a great
relevance in thermodynamics. Significant efforts have been devoted to
investigate the role of correlations in work extraction, among others. Here, we
derive a bound on the difference between global and local extractable work by
unitary operations (ergotropic gap), for bipartite separable states. Violation
of this bound necessarily certifies the presence of entanglement. This gap is
shown to be a monotone under LOCC assisted state transformations for pure
bipartite quantum states. Our criterion has an implication in witnessing the
dimension of a bipartite quantum state, with same local dimensions. On the
other hand, our result gives an operational meaning to the Nielsen-Kempe
disorder criterion. We also propose a schematic model to realize the
separability bound experimentally and to detect entanglement for a restricted
class of quantum states.
