Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference

Details Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference

2012-02-07

arxiv.org/abs/1202.1471v1

Physica Scripta 85, 025009 (2012)

Physics

Mathematical Physics

29 pages

Scientific paper

Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we investigate the possibility of describing the macroscopic behavior of complex systems in terms of the underlying statistical structure of their microscopic degrees of freedom by use of statistical inductive inference and information geometry. We review the Maximum Relative Entropy (MrE) formalism and the theoretical structure of the information geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special focus is devoted to the description of the roles played by the sectional curvature, the Jacobi field intensity and the information geometrodynamical entropy (IGE). These quantities serve as powerful information geometric complexity measures of information-constrained dynamics associated with arbitrary chaotic and regular systems defined on the statistical manifold. Finally, the application of such information geometric techniques to several theoretical models are presented.

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