Softening the Complexity of Entropic Motion on Curved Statistical Manifolds

TL;DR

This paper explores the information geometry and entropic dynamics of 3D and 2D Gaussian models, revealing how additional constraints can soften the system's chaotic behavior, with implications for understanding complexity in statistical manifolds.

Contribution

It introduces a comparison between 3D and 2D Gaussian models under information constraints, showing how chaos is reduced in the constrained 2D model.

Findings

Chaoticity is reduced in the 2D model compared to the 3D model.

Information geometric entropy (IGE) decreases with added constraints.

Jacobi vector field intensity indicates softened chaos in the constrained model.

Abstract

We study the information geometry and the entropic dynamics of a 3D Gaussian statistical model. We then compare our analysis to that of a 2D Gaussian statistical model obtained from the higher-dimensional model via introduction of an additional information constraint that resembles the quantum mechanical canonical minimum uncertainty relation. We show that the chaoticity (temporal complexity) of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE) and the Jacobi vector field intensity, is softened with respect to the chaoticity of the 3D Gaussian statistical model.