Local softening of information geometric indicators of chaos in statistical modeling in the presence of quantum-like considerations

TL;DR

This paper investigates how local constraints, inspired by quantum considerations, further weaken the chaotic behavior of information geometric indicators in statistical models, especially under correlation constraints.

Contribution

It extends previous work by analyzing the local softening of chaos indicators in correlated Gaussian models with quantum-like constraints.

Findings

Chaoticity is further weakened locally under correlation constraints.

Information geometric entropy decreases with added quantum-like constraints.

Quantum entanglement considerations relate to the physicality of the constraints.

Abstract

In a previous paper (C. Cafaro et al., 2012), we compared an uncorrelated 3D Gaussian statistical model to an uncorrelated 2D Gaussian statistical model obtained from the former model by introducing a constraint that resembles the quantum mechanical canonical minimum uncertainty relation. Analysis was completed by way of the information geometry and the entropic dynamics of each system. This analysis revealed that the chaoticity of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE), is softened or weakened with respect to the chaoticity of the 3D Gaussian statistical model due to the accessibility of more information. In this companion work, we further constrain the system in the context of a correlation constraint among the system's micro-variables and show that the chaoticity is further weakened, but only locally. Finally, the physicality of the constraints is briefly discussed, particularly in the context of quantum entanglement.