Information Geometry and Chaos on Negatively Curved Statistical Manifolds
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 Ms 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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