ABSTRACT The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive (classical) density functional theory approaches. Despite this, fundamental questions remain over why it is accurate and how one might include higher-order terms to improve accuracy. We derive the morphometric approach as the exact resummation of terms in the virial series, providing further justification of the approach. The resulting theory is less accurate than previous morphometric theories, but provides fundamental insights into the inclusion of higher-order terms and to extensions to mixtures of convex bodies of arbitrary shape.

中文翻译：

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受控膨胀硬体的形态热力学

摘要 形态计量学方法是将复杂溶质的化学势分解为纯几何项的强大工具。该方法已在硬球中证明了准确性，为相对昂贵的（经典）密度泛函理论方法提供了一种替代方法。尽管如此，基本问题仍然存在于为什么它是准确的以及如何包括高阶项以提高准确性。我们将形态测量方法推导出为维里级数中项的精确求和，为该方法提供了进一步的证明。由此产生的理论不如以前的形态测量理论准确，但提供了对高阶项的包含以及对任意形状凸体混合的扩展的基本见解。