The modelling of two-phase flows by multi-fluid models is an active research topic. Among the possible models, the Baer-Nunziato models [1] are usually closed by choosing the interfacial velocity equal toone of the phasic velocities. However, for the modelling of flows involving a large range of topologies, a more versatile approach consists in closing the interfacial velocity as the barycentric one, also called hydrodynamic mixture velocity. With this interfacial velocity, the mathematical closure for interfacial pressure, which allows for the correct treatment of shocks and to solve the Riemann problem, lead to an interfacial pressure that involves the phasic temperatures [2], even though the interfacial pressure plays a mechanical role rather than a thermal one. On the other hand, closures proposed by the fluid mechanics community [5], do not yield a conservation law for the the system’s entropy, and thus deprive the system of an admissible shock selection criterion. Alternatively, the theory of Hyperbolic Thermodynamically Compatible systems yields several classes of two-fluid models, which in the barotropic case are closely related to the Baer-Nunziato model [4]. Nevertheless, several attempts of their extension to non-barotropic flows have been conducted, but may lead to artificial heat exchanges proportional to the relative velocity. In this presentation, we propose a novel two-fluid full non-equilibrium model derived via the Stationary Action Principle. The new model involves an additional interfacial quantity compared to the existing approaches, namely the interfacial work. In the multi-dimensional setting, the model presents lift forces, which are also discussed. The model is fully closed and its closures for the interfacial quantities are directly provided by the variational principle [3]. In the one-dimensional setting, the model is shown to be hyperbolic, symmetrizable, and admits an entropy conservation law. Moreover, its non-conservative products yield uniquely defined jump conditions [3]. Numerical simulations illustrate the potentialities of the model