Incomplete equilibrium in long-range interacting systems

TL;DR

This paper investigates the statistical mechanics of long-range interacting systems, revealing how quasi-stationary states exhibit anomalous velocity distributions yet still conform to Boltzmann statistics within a specific sub-manifold.

Contribution

It introduces a framework to understand quasi-stationary states in long-range systems by identifying a nonequilibrium sub-manifold where Boltzmann-Gibbs statistics apply.

Findings

Quasi-stationary states have anomalous velocity distributions.

Boltzmann expression holds in a specific sub-manifold of phase space.

The nonequilibrium sub-manifold characterizes anomalous behavior.

Abstract

We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasi-stationary 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 sub-manifold of $\Gamma$-space characterizing the anomalous behavior and show that by restricting the Boltzmann-Gibbs approach to this sub-manifold we obtain the statistical mechanics of the quasi-stationary states.