Softening the Complexity of Entropic Motion on Curved Statistical Manifolds

Abstract

We study the information geometry and the entropic dynamics of a three-dimensional Gaussian statistical model. We then compare our analysis to that of a two-dimensional 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 two-dimensional 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 three-dimensional Gaussian statistical model.