  A generic feature of systems with long-range interactions is the presence of
{\it quasi-stationary} states with non-Gaussian single particle velocity
distributions. For the case of the Hamiltonian Mean Field (HMF) model, we
demonstrate that a maximum entropy principle applied to the associated Vlasov
equation explains known features of such states for a wide range of initial
conditions. We are able to reproduce velocity distribution functions with an
analytical expression which is derived from the theory with no adjustable
parameters. A normal diffusion of angles is detected and a new dynamical
effect, two oscillating clusters surrounded by a halo, is also found and
theoretically justified.
