Three hard spheres in a spherical cavity

Abstract

This work is devoted to furthering the understanding of few- and many-body inhomogeneous systems in the framework of the statistical mechanics of fluids. The three-body system consisting in three hard spheres (HS) confined in a spherical cavity at constant temperature is studied. Its canonical ensemble partition function and thermodynamic properties (such as the free energy, pressures, and fluid-substrate surface tension) are analytically obtained as a function of the cavity radius. This is the first time that a three-body fluid-like system is exactly solved. Symmetry relations between this system and its dual system composed of three HS surrounding a hard spherical object are analyzed. They allow to analytically obtain the canonical partition function of the dual system and its thermodynamic properties. Finally, the behavior of the many-body system of HS in contact with a hard spherical wall in the low density limit, is studied, focusing on the curvature dependence of the fluid-substrate surface tension and finding exact expressions for the Tolman's length and the second order term in curvature.