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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; in revised form: 21 October 2013 / Accepted: 22 October 2013 / Published: 28 October 2013
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.
Keywords: probability theory; Riemannian geometry; chaos; complexity; entropy
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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.
Giffin A, Ali SA, Cafaro C. Local Softening of Information Geometric Indicators of Chaos in Statistical Modeling in the Presence of Quantum-Like Considerations. Entropy. 2013; 15(11):4622-4633.
Giffin, Adom; Ali, Sean A.; Cafaro, Carlo. 2013. "Local Softening of Information Geometric Indicators of Chaos in Statistical Modeling in the Presence of Quantum-Like Considerations." Entropy 15, no. 11: 4622-4633.