Multipartite entanglement measures based on the thermodynamic framework

In this work, we introduce a unified method to characterize and measure multipartite entanglement using the framework of thermodynamics. A family of entanglement measures is proposed: ergotropic-gap concentratable entanglement. Furthermore, we establish that ergotropic-gap concentratable entanglement constitutes a well-defined entanglement measure within a specific parameter regime, satisfying key properties including continuity, majorization monotonicity, and monogamy. We demonstrate the utility of this measure by showing it effectively distinguishes between multiqubit Greenberger-Horne-Zeilinger states and W states. It also proves effective in detecting entanglement in specific classes of four-partite star quantum network states.