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.

8 pages, 4 figures. New version accepted for publication in Physica A

References in corpus (5)

• A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model
• Central limit behavior of deterministic dynamical systems
• Lynden-Bell and Tsallis distributions for the HMF model
• Hamiltonian dynamics reveals the existence of quasi-stationary states for long-range systems in contact with a reservoir
• Incomplete equilibrium in long-range interacting systems

Cited by in corpus (6)

• A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model
• Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions
• Nonextensive Statistical Analysis of Meteor Showers and Lunar Flashes
• Relationship between nonlinearities and thermalization in classical open systems: The role of the interaction range
• Computational Statistical Mechanics of a confined, three-dimensional Coulomb gas
• Conditional maximum entropy and Superstatistics