Note: An exact scaling relation for truncatable free energies of polydisperse hard-sphere mixtures

TL;DR

This paper proves an exact scaling relation for truncatable free energies in polydisperse hard-sphere mixtures, simplifying the dependence on size distribution moments and reducing the effective degrees of freedom.

Contribution

It introduces a rigorous scaling relation that reduces the complexity of modeling truncatable free energies in polydisperse systems.

Findings

Proves an exact scaling relation for truncatable free energies.

Reduces the effective degrees of freedom to K-2.

Provides a theoretical foundation for simplified modeling.

Abstract

A theoretical model for polydisperse systems of hard spheres is said to be truncatable when the excess free energy depends on the size distribution through a finite number $K$ of moments. This Note proves an exact scaling relation for truncatable free energies, which allows to reduce the effective degrees of freedom to $K-2$ independent combinations of the moments.