Information Geometry and Chaos on Negatively Curved Statistical Manifolds

Details Information Geometry and Chaos on Negatively Curved Statistical Manifolds Information Geometry and Chaos on Negatively Curved Statistical Manifolds

2008-10-25

arxiv.org/abs/0810.4622v1

AIP Conf. Proc. 954, 175 (2007)

Physics

Mathematical Physics

7 pages, presented at MaxEnt2007, the 27th International Workshop on Bayesian Inference and Maximum Entropy Methods, Saratoga

Scientific paper

10.1063/1.2821260

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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