| Description |
The paper explores the mechanism responsible for the ergodicity breaking in a system with long-range forces, namely the HMF (Hamtiltonian Mean-Field) Model. In thermodynamic limit such systems do not evolve to the Boltzmann-Gibbs equilibrium, but become trapped in an out-of-equilibrium quasi-stationary-state (QSS), which can be described by Lyden-Bell statistics. However, they show that only if the initial distribution satisfies a specific constraint - a generalized virial condition - theQSS 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 (relaxation to the Lyden-Bell state is incomplete).
References:
http://arxiv.org/abs/1202.1810
Lynden-Bell and Tsallis distributions for the HMF model, P. H. Chanavis, EJPB 53, 4
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