Vanishing largest Lyapunov exponent and Tsallis entropy
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In this article, the authors present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamic aspects which can be effectively described by the Tsallis entropy.Abstract:
We present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamic aspects which can be effectively described by the Tsallis entropy. We rely on a comparison of the generalised additivity of the Tsallis entropy versus the ordinary additivity of the BGS entropy. We translate this comparison, in metric terms, by using an effective hyperbolic metric on the configuration/phase space for the Tsallis entropy versus the Euclidean one in the case of the BGS entropy. Solving the Jacobi equation for such hyperbolic metrics effectively sets the largest Lyapunov exponent computed, with respect to the corresponding Euclidean metric, to zero. This conclusion is in agreement with all currently known results on systems that have a simple asymptotic behaviour, and are described by the Tsallis entropy.read more
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