  We study the one-particle von Neumann entropy of a system of N hard-core
anyons on a ring. The entropy is found to have a clear dependence on the
anyonic parameter which characterizes the generalized fractional statistics
described by the anyons. This confirms the entanglement as a valuable measure
to investigate topological properties of quantum states. Furthermore, we
determine analytically the large N asymptotics of the anyonic one-particle
density matrix. The formula presented here generalizes the Lenard formula
obtained for a system of N hard-core bosons. Finally, we present a numerical
analysis which confirms the analytical results and provides additional insight
into the problem under consideration.
