I will discuss identical particles in 2-dimensions. In 3 and higher dimensions there are two types of identical particle fermions and bosons. As is well known they have very different thermodynamic properties. Free fermions have a degeneracy pressure due to the Pauli exclusion principle. Bosons do not have a degeneracy pressure. The Lieb-Thirring inequality is an elegant expression of the degeneracy pressure. In 2 dimensions there are particles of intermediate statistics called anyons, described by a statistics parameter running from 0 to 1 (0 being bosons and 1 being fermions). I will show that free anyons satisfy a Lieb-Thirring inequality if the statistics parameter is rational with odd numerator. This is joint work with Douglas Lundholm.