Entropic dynamical models with unstable jacobi fields

The instability of an entropic dynamical model is considered via Jacobi vector field and the Lyapunov exponent. From the viewpoint of information geometry, geometric structure of the statistical manifold underlying this model is investigated, and we conclude that it is a manifold with constant negative scalar curvature. By use of the Jacobi vector field associated with the geodesics, we study the asymptotic behavior of the geodesic spread on the statistical manifold and reach that it is described by an exponentially divergent Jacobi vector field with respect to time. A positive Lyapunov exponent is also obtained, that explains the local instability of the system as well. Furthermore, submanifolds are studied similarly.