Out-of-equilibrium states as statistical equilibria of an effective   dynamics
  We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical equilibria of an effective dynamics, which is derived using averaging techniques. This simple behavior might be a prototype of others observed in more complicated systems with long-range interactions, like two-dimensional incompressible fluids or self-gravitating systems. 
Julien Barre', Freddy Bouchet, Thierry Dauxois, Stefano Ruffo