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Entropy 2013, 15(11), 4622-4633; doi:10.3390/e15114622

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

1,* , 2,3
1 Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA 2 International Institute for Theoretical Physics and Mathematics, Einstein-Galilei, Prato 59100, Italy 3 Department of Basic and Social Sciences, Albany College of Pharmacy and Health Sciences, Albany,NY 12208, USA 4 Max-Planck Institute for the Science of Light, Erlangen D-91058, Germany 5 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)
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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.
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).

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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.

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