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.
Keywords
Cite
@article{arxiv.0810.4622,
title = {Information Geometry and Chaos on Negatively Curved Statistical Manifolds},
author = {Carlo Cafaro},
journal= {arXiv preprint arXiv:0810.4622},
year = {2009}
}
Comments
7 pages, presented at MaxEnt2007, the 27th International Workshop on Bayesian Inference and Maximum Entropy Methods, Saratoga (NY, USA) (July-2007)