A self-consistent thermodynamic formalism is developed for the treatment of the equilibrium of systems, some of whose parameters vary continuously from place to place. The method is specially designed for the description of transition interfaces separating two phases. The energy per unit volume is assumed to depend explicitly on the space derivatives of the molecule densities. Equilibrium conditions are obtained for the appropriate internal variables of the system, and all externally measurable intensive variables are uniquely defined by a variational procedure.

• Received 11 August 1958

DOI:https://doi.org/10.1103/PhysRev.113.412