  We consider the entropy of polydisperse chains placed on a lattice. In
particular, we study a model for equilibrium polymerization, where the
polydispersivity is determined by two activities, for internal and endpoint
monomers of a chain. We solve the problem exactly on a Bethe lattice with
arbitrary coordination number, obtaining an expression for the entropy as a
function of the density of monomers and mean molecular weight of the chains. We
compare this entropy with the one for the monodisperse case, and find that the
excess of entropy due to polydispersivity is identical to the one obtained for
the one-dimensional case. Finally, we obtain an exponential distribution of
molecular weights.
