Ergodicity Breaking and Parametric Resonances in Systems with Long-Range   Interactions
  We explore the mechanism responsible for the ergodicity breaking in systems with long-range forces. In thermodynamic limit such systems do not evolve to the Boltzmann-Gibbs equilibrium, but become trapped in an out-of-equilibrium quasi-stationary-state. Nevertheless, we show that if the initial distribution satisfies a specific constraint - a generalized virial condition - the quasi- stationary-state is very close to ergodic and can be described by Lynden-Bell statistics. On the other hand if the generalized virial condition is violated, parametric resonances are excited, leading to chaos and ergodicity breaking. 
Fernanda P. da C. Benetti, Tarc\'isio N. Teles, Renato Pakter, and Yan   Levin
cond-mat.stat-mech physics.plasm-ph