How to predict polydisperse hard-sphere mixture behavior using maximally equivalent tridisperse systems

Polydisperse hard sphere mixtures have equilibrium properties which essentially depend on the number density and a reduced number $K$ of moments of the size distribution function. Such systems are equivalent to other systems with different size distributions if the $K$ moments are matched. In particular, a small number $s$ of components, such that $2s-1=K$ is sufficient to mimic systems with continuous size distributions. For most of the fluid phase $K=3$ moments ($s=2$ components) are enough to define an equivalent system, while in the glassy states one needs $K=5$ moments ($s=3$ components) to achieve good agreement between the polydisperse and its maximally-equivalent tridisperse system. With $K=5$ matched moments they are also close in number- and volume-fractions of rattlers. Finally, also the jamming density of maximally-equivalent jammed packings is very close, where the tiny differences can be explained by the distribution of rattlers.