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

TL;DR

This paper examines the non-Boltzmannian characteristics of quasi-stationary states in long-range interacting systems, specifically the Hamiltonian Mean Field model, and discusses implications for generalized $q$-statistics.

Contribution

It presents a theorem ruling out Boltzmann-Gibbs exponential weights in the microscopic configuration space of the HMF model.

Findings

Excludes Boltzmann-Gibbs exponential weight in the HMF model.

Comments on recent related research by Baldovin and Orlandini.

Highlights ongoing debate on applying generalized $q$-statistics to long-range 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.