Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature

Abstract

A new information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) 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 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.

arXiv comment8 pages, final version accepted for publication

References in corpus (14)

• Decoherence, Chaos, and the Second Law
• Updating Probabilities
• Riemannian theory of Hamiltonian chaos and Lyapunov exponents
• Quantum chaos: a decoherent definition.
• Maximum Entropy and Bayesian Data Analysis: Entropic Priors
• The Generalized Jacobi Equation
• Consistency, Amplitudes and Probabilities in Quantum Theory
• Jacobi Fields on Statistical Manifolds of Negative Curvature
• Relative Entropy and Inductive Inference
• Entropic Dynamics
• Hypersensitivity and chaos signatures in the quantum baker's maps
• Consistency and Linearity in Quantum Theory
• Information Geometry and Chaos on Negatively Curved Statistical Manifolds
• An Application of Reversible Entropic Dynamics on Curved Statistical Manifolds

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