On first-order thermodynamic equilibrium conditions for fluid-fluid and solid-phase interfaces

Starting from the constrained variational formulation of Larch'e and Cahn for solids in contact with fluids, a unified thermodynamic framework for such systems is developed. Both bulk and interfacial equilibrium conditions arise as stationarity conditions of a single thermodynamic functional. While earlier theory neglects a full treatment of interfacial contributions and therefore cannot describe systems in which surface effects are significant, the present formulation incorporates interfacial thermodynamics directly into the variational principle. The framework is introduced first for fluid-fluid systems to establish the underlying mathematical structure, and is then extended to solid-fluid interfaces. Within this setting, classical equilibrium relations for heterogeneous systems emerge naturally from different classes of admissible variations, providing a common theoretical basis for bulk, interfacial, and configurational thermodynamics.