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.