Geometrical Aspects of the Penetrable-Sphere Model

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Abstract
It is shown that the potential energy of interaction in the penetrable-sphere model may be decomposed into negative two-body, four-body, ··· potentials corresponding to attractive forces among the molecules, and positive three-body, five-body, ··· potentials corresponding to repulsive forces. These and related aspects of the interaction energy imply, via the potential distribution theory, a number of inequalities among the thermodynamic functions of the model fluid. It is also shown that the interaction potential is a homogeneous function of the coordinates of the molecular centers and of the sphere radius, from which there follow two virial-like relations. The latter yield a geometric criterion for phase equilibrium in the model, as well as additional thermodynamic inequalities.

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