Vanishing largest Lyapunov exponent and Tsallis entropy

Details Vanishing largest Lyapunov exponent and Tsallis entropy Vanishing largest Lyapunov exponent and Tsallis entropy

2012-03-13

arxiv.org/abs/1203.2707v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, No figures. LaTex2e. Some overlap with arXiv:1104.4869 The present paper is less speculative, more concrete, concise

Scientific paper

We present a geometric, model-independent, argument that explains why the Tsallis entropy describes dynamical systems having vanishing largest Lyapunov exponent. We employ the Jacobi/geodesic deviation equation for an effective negative curvature Riemannian metric reflecting the Tsallis entropy composition property, whose solution gives the desired result. Extending the essential parts of the argument from Riemannian manifolds to CAT(k), k<0 spaces, we see that the conclusion remains valid in the case of interacting systems described by different entropic parameters. This conclusion is in agreement with all currently known results.

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