Statistical mechanics of unbound two-dimensional self-gravitating systems

We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two-dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the Maxwell-Boltzmann distribution. The time taken to reach the thermodynamic equilibrium, however, scales with the number of particles. In the thermodynamic limit, N -> infinity at fixed total mass, an equilibrium state is never reached and the system becomes trapped in a non-ergodic stationary state. An analytical theory is presented which allows us to quantitatively describe this final stationary state, without any adjustable parameters.