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The morphometric approach is a powerful ansatz for decomposing the chemicalpotential for a complex solute into purely geometrical terms. This method hasproven accuracy in hard spheres, presenting an alternative to comparativelyexpensive (classical) density functional theory approaches. Despite this,fundamental questions remain over why it is accurate and how one might includehigher-order terms to improve accuracy. We derive the morphometric approach asthe exact resummation of terms in the virial series, providing furtherjustification of the approach. The resulting theory is less accurate thanprevious morphometric theories, but provides fundamental insights into theinclusion of higher-order terms and to extensions to mixtures of convex bodiesof arbitrary shape.

Morphological thermodynamics for hard bodies from a controlled expansion