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

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.

8 pages, improved v2, Invited Contribution for a Special Issue of Entropy on "Distance in Information and Statistical Physics"

References in corpus (7)

• Updating Probabilities
• Quantum phases with differing computational power
• Entropic Dynamics
• A violation of the uncertainty principle implies a violation of the second law of thermodynamics
• Open timelike curves violate Heisenberg's uncertainty principle
• Standard forms and entanglement engineering of multimode Gaussian states under local operations
• Information geometric complexity of entropic motion on curved statistical manifolds

Cited by in corpus (6)

• Information geometric methods for complexity
• Heisenberg and entropic uncertainty measures for large-dimensional harmonic systems
• Theoretical investigations of an information geometric approach to complexity
• Notions of the ergodic hierarchy for curved statistical manifolds
• Hermite-Gaussian model for quantum states
• An information geometric perspective on the complexity of macroscopic predictions arising from incomplete information