The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models

TL;DR

This paper analytically investigates how microcorrelations influence the asymptotic behavior of information geometric complexity in Gaussian models, revealing that correlations accelerate macrostate compression and affect system complexity.

Contribution

It provides the first analytical analysis of how microcorrelations impact the asymptotic behavior of information geometric complexity in Gaussian models.

Findings

Microcorrelations cause a power law decay in IGC.

Correlations lead to faster macrostate compression.

Microcorrelations influence the macro-level complexity dynamics.

Abstract

We present an analytical computation of the asymptotic temporal behavior of the information geometric complexity (IGC) of finite-dimensional Gaussian statistical manifolds in the presence of microcorrelations (correlations between microvariables). We observe a power law decay of the IGC at a rate determined by the correlation coefficient. It is found that microcorrelations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored by the system at a faster rate than that observed in absence of microcorrelations. This finding uncovers an important connection between (micro)-correlations and (macro)-complexity in Gaussian statistical dynamical systems.