The geometric structures and instability of entropic dynamical models. (English) Zbl 1257.53024
From the text: In this paper, we study two entropic dynamical (ED) models, 2D and 3D statistical manifolds \(\mathcal M_1\) and \(\mathcal M_2\) which serve as the stage on which the entropic dynamics evolves. The structure is obtained from the viewpoint of information geometry. Using the obtained Riemannian curvature tensor or Christoffel symbols we get the Jacobi vector field associated with the geodesic deviation equations on the manifolds, the asymptotic behavior of which conversely indicates the behavior of the geodesics. These are concluded for the two models, respectively as follows: first-order linearly divergent instability for ED1, and exponential instability for ED2. This progress is extremely special and important, based on that statistical curvature is used to characterize the chaos of a given entropic dynamical model, rather than only quantities on the associated manifolds.
Reviewer: A. Neagu (Iaşi)
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