Incomplete equilibrium in long-range interacting systems

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' Gamma space. We identify the nonequilibrium submanifold of Gamma 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.