Entropy of particle packings: An illustration on a toy model

A toy model of particle packing is presented, which consists in arranging hexagons on a triangular lattice according to local stability rules. The number of stable packings is analytically computed and found to grow exponentially with the size of the lattice, which illustrates the concept of packing entropy first proposed by Edwards and collaborators. The analysis is carried out for both the monodispersed case and the more interesting, i.e. more disordered, bidispersed case.