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 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.

7 pages, presented at MaxEnt2007, the 27th International Workshop on Bayesian Inference and Maximum Entropy Methods, Saratoga (NY, USA) (July-2007)

References in corpus (3)

• Updating Probabilities
• Jacobi Fields on Statistical Manifolds of Negative Curvature
• Hypersensitivity and chaos signatures in the quantum baker's maps

Cited by in corpus (4)

• Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?
• Information Geometry, Inference Methods and Chaotic Energy Levels Statistics
• Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature
• Geometrodynamics of Information on Curved Statistical Manifolds and its Applications to Chaos