Geometrodynamics of Information on Curved Statistical Manifolds and its Applications to Chaos

Abstract

A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of chaoticity is proposed. The general classical formalism is illustrated in a relatively simple example. 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. An information-geometric analogue of the Zurek-Paz quantum chaos criterion in the classical reversible limit is proposed. This analogy is illustrated applying the IGAC to a set of n-uncoupled three-dimensional anisotropic inverted harmonic oscillators characterized by a Ohmic distributed frequency spectrum.

arXiv comment17 pages

References in corpus (9)

• Decoherence, Chaos, and the Second Law
• Updating Probabilities
• Riemannian theory of Hamiltonian chaos and Lyapunov exponents
• Maximum Entropy and Bayesian Data Analysis: Entropic Priors
• Entropic Dynamics
• Jacobi Fields on Statistical Manifolds of Negative Curvature
• From Information Geometry to Newtonian Dynamics
• Hypersensitivity and chaos signatures in the quantum baker's maps
• Information Geometry and Chaos on Negatively Curved Statistical Manifolds

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• An information geometric perspective on the complexity of macroscopic predictions arising from incomplete information
• The Information Geometry of Chaos
• Reexamination of an Information Geometric Construction of Entropic Indicators of Complexity