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The principles of classical mechanics have shown that the inertial quality of mass is characterized by the kinetic energy. This, in turn, establishes the connection between geometry and mechanics. We aim to exploit such a fundamental principle for information geometry entering the realm of mechanics. According to the modification of curve energy stated by Amari and Nagaoka for a smooth manifold $mathrm{M}$ endowed with a dual structure $(mathrm{g}, abla, abla^*)$, we consider $ abla$ and $ abla^*$ kinetic energies. Then, we prove that a recently introduced canonical divergence and its dual function coincide with Hamilton principal functions associated with suitable Lagrangian functions when $(mathrm{M},mathrm{g}, abla, abla^*)$ is dually flat. Corresponding dynamical systems are studied and the tangent dynamics is outlined in terms of the Riemannian gradient of the canonical divergence. Solutions of such dynamics are proved to be $ abla$ and $ abla^*$ geodesics connecting any two points sufficiently close to each other. Application to the standard Gaussian model is also investigated.
A recent canonical divergence, which is introduced on a smooth manifold $mathrm{M}$ endowed with a general dualistic structure $(mathrm{g}, abla, abla^*)$, is considered for flat $alpha$-connections. In the classical setting, we compute such a canoni
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with the Kullback
We consider the Grover walk model on a connected finite graph with two infinite length tails and we set an $ell^infty$-infinite external source from one of the tails as the initial state. We show that for any connected internal graph, a stationary st
Superintegrable systems on a symplectic manifold conventionally are considered. However, their definition implies a rather restrictive condition 2n=k+m where 2n is a dimension of a symplectic manifold, k is a dimension of a pointwise Lie algebra of a
In this paper, we consider the scattering theory for acoustic-type equations on non-compact manifolds with a single flat end. Our main purpose is to show an existence result of non-scattering energies. Precisely, we show a Weyl-type lower bound for t