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

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.

arXiv commentCommunication at next2003, Second Sardinian International Conference on News and Expectations in Thermostatistics, Villasimius (Cagliari) Italy, 21st-28th September 2003. Submitted to Physica A. Elsevier Latex, 17 pages, 8 figures

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• Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach
• Long-range interactions, doubling measures and Tsallis entropy
• Aging at the edge of chaos: Glassy dynamics and nonextensive statistics
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• Two-dimensional dissipative maps at chaos threshold: Sensitivity to initial conditions and relaxation dynamics
• Intermittency at critical transitions and aging dynamics at edge of chaos
• Effective temperatures for single particle system under dichotomous noise
• On time and ensemble averages in quasistationary state of low-dimensional Hamiltonian maps
• Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps