Statistical entropy of a binary hard-sphere mixture: the low-density limit

We have studied the virial expansion of the configurational entropy of a binary mixture of unequal hard spheres as a function of the diameter ratio and of the relative concentration of the two species. The entropy was analysed as a sum of two terms: a pair term, which arises from two-particle spatial correlations, and a residual contribution that is associated with correlations involving more than two particles. We discuss the behaviour of this last quantity in the regime of strongly asymmetric sizes and concentrations with specific regard to the onset of the mechanism leading to phase separation at a thermodynamic level.