Nonequilibrium stationary states of 3D self-gravitating systems
  Three dimensional self-gravitating systems do not evolve to thermodynamic equilibrium, but become trapped in nonequilibrium quasistationary states. In this Letter we present a theory which allows us to a priori predict the particle distribution in a final quasistationary state to which a self-gravitating system will evolve from an initial condition which is isotropic in particle velocities and satisfies a virial constraint 2K=-U, where K is the total kinetic energy and U is the potential energy of the system. 
Fernanda P.C. Benetti, Ana C. Ribeiro-Teixeira, Renato Pakter and Yan   Levin
cond-mat.stat-mech astro-ph.GA