Statistical descriptions of nonlinear systems at the onset of chaos

Details Statistical descriptions of nonlinear systems at the onset of chaos Statistical descriptions of nonlinear systems at the onset of chaos

2005-11-30

arxiv.org/abs/cond-mat/0511736v1

Physica A365:252-257,2006

Physics

Condensed Matter

Statistical Mechanics

RevTeX preprint 10 pages, 4 figures, to appear in The European Physical Journal B

Scientific paper

10.1016/j.physa.2006.01.007

Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of the corresponding asymptotic sensitivity to initial conditions \lambda. The statistical formalism and the equality K=\lambda can be extended to weakly chaotic systems by suitable and corresponding generalizations of the logarithm and of the entropy. Using the logistic map as a test case we consider a wide class of deformed statistical description which includes Tsallis, Abe and Kaniadakis proposals. The physical criterion of finite-entropy growth K strongly restricts the suitable entropies. We study how large is the region in parameter space where the generalized description is useful.

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