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arXiv · 0810.4622

Information Geometry and Chaos on Negatively Curved Statistical Manifolds

Carlo Cafaro
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Abstract

A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s} underlying an ED Gaussian model describing an arbitrary system of 3N non-interacting degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively.

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Carlo Cafaro. 2008-10-25. Information Geometry and Chaos on Negatively Curved Statistical Manifolds. https://doi.org/10.1063/1.2821260

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