Prediction of polydisperse hard-sphere mixture behavior using tridisperse systems

How many state-variables are needed to predict the equation of state and the jamming density of polydisperse mixtures in glassy, non-equilibrium compressed states? We propose to define equivalent and maximally equivalent systems as those that match three and five moments of a given polydisperse size distribution, respectively. Fluids can be represented well by an equivalent system with only s = 2 components (bidisperse). As little as s = 3 components (tridisperse) are enough to achieve a maximally equivalent system. Those match macroscopic properties in glassy states, but also the volume fraction of rattlers, suggesting strong microstructural equivalency too. For many soft and granular systems, tridisperse, maximally equivalent systems allow for a closed analytical treatment and well-controlled industrial applications, while our proposal waits for experimental validation.