Hamilton-Jacobi approach to Potential Functions in Information Geometry

Abstract

The search for a potential function $S$ allowing to reconstruct a given metric tensor $g$ and a given symmetric covariant tensor $T$ on a manifold $\mathcal{M}$ is formulated as the Hamilton-Jacobi problem associated with a canonically defined Lagrangian on $T\mathcal{M}$. The connection between this problem, the geometric structure of the space of pure states of quantum mechanics, and the theory of contrast functions of classical information geometry is outlined.

16 pages. A discussion on the Kullback-Leibler divergence has been added. To appear in Journal of Mathematical Physics

References in corpus (2)

• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
• Metric on the space of quantum states from relative entropy. Tomographic reconstruction

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• Lagrangian and Hamiltonian Mechanics for Probabilities on the Statistical Manifold
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• Information geometry on groupoids: the case of singular metrics
• Towards a Canonical Divergence within Information Geometry
• Generalised Potential Functions in Differential Geometry and Information Geometry
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• Dynamical Systems induced by Canonical Divergence in dually flat manifolds
• Hamilton-Jacobi Theory and Information Geometry