A theorem for inhomogeneous systems: The generalization of the nucleation theorem

We show that the validity of the nucleation theorem transcends the phenomenon of nucleation and extends to all equilibrium systems containing local nonuniform density distributions stabilized by external fields, and that it remains valid down to the molecular level. This result is tested by the application of exact theory at the molecular level and is shown to be valid in all the cases for which we have been able to complete such an exact analysis. These cases include cavities and clusters in hard rod fluids, as well as the molecular excesses associated with the "atmospheres" of molecules in single and multicomponent fluids. We show that, at the molecular level, the theorem can be associated with the compressibility equation of state and, at the macroscopic level, with the Gibbs adsorption equation. It is thus a relation of great power and should be useful in many contexts. (C) 2001 American Institute of Physics.