INVERSE PROBLEM IN CLASSICAL STATISTICAL MECHANICS

Examples of inverse solutions for the effective additive pair potential from guessed equilibrium pair distribution are given for the Percus-Yevick, hypernetted-chain, and Stillinger-Buff (with an inexact mean-density closure relation) equations. The found potentials depend on density and temperature and the potential for a given guessed distribution predicted by the Percus-Yevick theory is always smaller than that from the hypernetted chain equation. The exact inverse problem of determining the potential from the nonuniform pair distribution is formulated via the Stillinger-Buff equation and the difficulties in solving this problem are indicated. In a related inverse problem we characterize the possible equations of state consistent with the assumption that the potential of mean force of the fluid is directly proportional to the, possibly density dependent, pair potential. © 1969 The American Physical Society.