Statistical descriptions of nonlinear systems at the onset of chaos

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

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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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