Entropy driven demixing: why?

An exact solution is found for a model of N different, in general, hard convex bodies moving without rotation in independent cells of hard walls and fixed total volume. It is shown that the entropy of the system is maximal when the cell shapes are the same as the body shapes, and their volumes depend on the body sizes in a universal way. The obtained distribution of volume into cells indicates the mechanism of phase separation in mixtures of hard bodies of different sizes and/or shapes. A planar system of hard squares and equilateral triangles of equal sides is considered as an example. An argument is presented that these bodies do not mix near close packing