Information Geometry and Chaos on Negatively Curved Statistical Manifolds

TL;DR

This paper introduces an information-geometric framework for analyzing chaos on curved statistical manifolds, linking entropy growth and divergence of trajectories to underlying geometric properties, applicable to classical and quantum chaos.

Contribution

It proposes a novel information-geometric approach to chaotic dynamics and introduces an analogue of the quantum chaos criterion within this framework.

Findings

Hyperbolicity of the statistical manifold leads to linear entropy growth.

Exponential divergence of Jacobi fields indicates chaos.

The approach bridges classical and quantum chaos features.

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.