Exact Definition of Quasi-Thermodynamic Point Functions in Statistical Mechanics

The present note provides a rigorous definition and justification for the use of a ``local'' or ``point'' chemical potential (or activity coefficient), constant in value, in a transition region between two phases, or in the immediate neighborhood of a particular molecule or ion in a homogeneous fluid or solution. In the transition case, other quasi-thermodynamic point functions are also given exact definition; for example, the Helmholtz free energy, internal energy, and entropy. Possible applications, past and future, include the theory of liquids, solutions, electrolytes, and surface tension.