Nonequilibrium phase transitions and violent relaxation in the   Hamiltonian Mean Field model
  We discuss the nature of nonequilibrium phase transitions in the Hamiltonian Mean Field model using detailed numerical simulation of the Vlasov equation and molecular dynamics. Starting from fixed magnetization waterbag initial distributions and varying the energy, the states obtained after a violent relaxation undergoes a phase transition from magnetized to non-magnetized states when going from lower to higher energies. The phase transitions are either first order or composed by a cascade of phase reentrances. This result is at variance with most previous results in the literature mainly based in Lynden-Bell theory of violent relaxation. The latter is a rough approximation and consequently not suited for an accurate description of nonequilibrium phase transition in long range interacting systems. 
M. Rocha Filho, M. A. Amato and A. Figueiredo
cond-mat.stat-mech