A maximum entropy principle explains quasi-stationary states in systems   with long-range interactions: the example of the Hamiltonian Mean Field model
  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. 
Andrea Antoniazzi, Duccio Fanelli, Julien Barr\'e, Pierre-Henri   Chavanis, Thierry Dauxois, Stefano Ruffo