In quantum mechanics, stringnet condensed states - a family of prototypical
states exhibiting non-trivial topological order - can be classified via their
long-range entanglement properties, in particular topological corrections to
the prevalent area law of the entanglement entropy. Here we consider classical
analogs of such stringnet models whose partition function is given by an
equal-weight superposition of classical stringnet configurations. Our analysis
of the Shannon and Renyi entropies for a bipartition of a given system reveals
that the prevalent volume law for these classical entropies is augmented by
subleading topological corrections that are intimately linked to the anyonic
theories underlying the construction of the classical models. We determine the
universal values of these topological corrections for a number of underlying
anyonic theories including su(2)_k, su(N)_1, and su(N)_2 theories
