Geometric thermodynamic fields and the generalized ensemble in colloidal physics.

The statistical geometry of hard-sphere mixtures, as defined by Speedy and Reiss, is found to lead to a sum rule that is identical in form to the fundamental equation of the generalized ensemble. This leads one to conjecture the specific form of a set of thermodynamic fields entirely defined by ensemble averages of geometric properties of the configurations. The potential for a direct physical understanding of these quantities is discussed and it is noted that they could, therefore, be of crucial significance to our future understanding of colloidal physics. In the presence of an ideal wall, an analogous sum rule is obtained in terms of interfacial geometric properties (the available surface area for insertions at the wall). For this case, which generalizes beyond hard-sphere models, there exists an obvious physical interpretation involving complete wetting at the ideal wall.