Next Article in Journal
Law of Multiplicative Error and Its Generalization to the Correlated Observations Represented by the q-Product
Previous Article in Journal
On the Diversity Constraints for Portfolio Optimization
Previous Article in Special Issue
Correlation Distance and Bounds for Mutual Information
Article Menu

Export Article

Open AccessArticle
Entropy 2013, 15(11), 4622-4633;

Local Softening of Information Geometric Indicators of Chaos in Statistical Modeling in the Presence of Quantum-Like Considerations

Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA
International Institute for Theoretical Physics and Mathematics, Einstein-Galilei, Prato 59100, Italy
Department of Basic and Social Sciences, Albany College of Pharmacy and Health Sciences, Albany,NY 12208, USA
Max-Planck Institute for the Science of Light, Erlangen D-91058, Germany
Institute of Physics, Johannes Gutenberg University, Mainz 55128, Germany
Author to whom correspondence should be addressed.
Received: 8 September 2013 / Revised: 21 October 2013 / Accepted: 22 October 2013 / Published: 28 October 2013
(This article belongs to the Special Issue Distance in Information and Statistical Physics Volume 2)
Full-Text   |   PDF [205 KB, uploaded 24 February 2015]


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. View Full-Text
Keywords: probability theory; Riemannian geometry; chaos; complexity; entropy probability theory; Riemannian geometry; chaos; complexity; entropy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

Giffin, A.; Ali, S.A.; Cafaro, C. Local Softening of Information Geometric Indicators of Chaos in Statistical Modeling in the Presence of Quantum-Like Considerations. Entropy 2013, 15, 4622-4633.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top