Incomplete equilibrium in long-range interacting systems

Abstract

We use Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasistationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution, we find that the central limit theorem implies the Boltzmann expression in Gibbs' Γ space. We identify the nonequilibrium submanifold of Γ space characterizing the anomalous behavior and show that by restricting the Boltzmann-Gibbs approach to this submanifold we obtain the statistical mechanics of the quasistationary states. © 2006 The American Physical Society.