Ubiquity of metastable-to-stable crossover in weakly chaotic dynamical systems

TL;DR

This paper compares various weakly chaotic dynamical systems, highlighting the universal presence of metastable states and their crossover to equilibrium, linked to nonextensive statistical mechanics.

Contribution

It demonstrates the ubiquity of metastable-to-stable crossover phenomena across diverse weakly chaotic systems and connects these behaviors to nonextensive statistical mechanics.

Findings

Metastable states are common in all studied systems.

Crossover to equilibrium occurs universally in these systems.

Behavior is linked to features of nonextensive statistical mechanics.

Abstract

We present a comparative study of several dynamical systems of increasing complexity, namely, the logistic map with additive noise, one, two and many globally-coupled standard maps, and the Hamiltonian Mean Field model (i.e., the classical inertial infinitely-ranged ferromagnetically coupled XY spin model). We emphasize the appearance, in all of these systems, of metastable states and their ultimate crossover to the equilibrium state. We comment on the underlying mechanisms responsible for these phenomena (weak chaos) and compare common characteristics. We point out that this ubiquitous behavior appears to be associated to the features of the nonextensive generalization of the Boltzmann-Gibbs statistical mechanics.