Characterizing bipartite entanglement via the ergotropic gap

The existence of quantum entanglement implies a non-vanishing thermodynamic quantity termed an ergotropic gap (EG). Our goal in this work is to characterize entanglement from the perspective of the ergotropic gap. We firstly define the passive-state energy of the marginals as an entanglement monotone named EG entanglement, additionally, we derive an analytical formula for two-qubit entangled systems. Another interesting result is the monogamy relation for the EG entanglement, which indicates that the shareability of bipartite entanglement in multipartite entangled systems is bounded by the amount of entanglement. Finally, we show that a necessary condition for an n-qubit pure state is that all marginal EG entanglements should satisfy polygon inequalities. These results reveal a new understanding of entanglement from the view of thermodynamics.