Weak Chaos from Tsallis Entropy

Abstract

We present a geometric, model-independent, argument that aims to explain why the Tsallis entropy describes systems exhibiting "weak chaos", namely systems whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument relies on properties of a deformation map of the reals induced by the Tsallis entropy, and its conclusion agrees with all currently known results.

19 pages, Standard LaTeX2e, v2: addition of the last paragraph in Section 4. Three additional refs. To be published in QScience Connect

References in corpus (5)

• Generalized canonical ensembles and ensemble equivalence
• Long-range correlations and ensemble inequivalence in a generalized ABC model
• Distributivity and deformation of the reals from Tsallis entropy
• Tsallis entropy induced metrics and CAT(k) spaces
• Some Open Points in Nonextensive Statistical Mechanics

Cited by in corpus (4)

• Long-range interactions, doubling measures and Tsallis entropy
• Vanishing largest Lyapunov exponent and Tsallis entropy
• Ricci curvature, isoperimetry and a non-additive entropy
• Entropies from coarse-graining: convex polytopes vs. ellipsoids