On the non-Boltzmannian nature of quasi-stationary states in long-range interacting systems

Abstract

We discuss the non-Boltzmannian nature of quasi-stationary states in the Hamiltonian Mean Field (HMF) model, a paradigmatic model for long-range interacting classical many-body systems. We present a theorem excluding the Boltzmann-Gibbs exponential weight in Gibbs $\Gamma$-space of microscopic configurations, and comment a paper recently published by Baldovin and Orlandini (2006). On the basis of the points here discussed, the ongoing debate on the possible application, within appropriate limits, of the generalized $q$-statistics to long-range Hamiltonian systems remains open.