  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.
