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arXiv · 1711.01129

Hamilton-Jacobi Theory and Information Geometry

Florio M. Ciaglia·Fabio Di Cosmo·Giuseppe Marmo
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Abstract

Recently, a method to dynamically define a divergence function $D$ for a given statistical manifold $(\mathcal{M}\,,g\,,T)$ by means of the Hamilton-Jacobi theory associated with a suitable Lagrangian function $\mathfrak{L}$ on $T\mathcal{M}$ has been proposed. Here we will review this construction and lay the basis for an inverse problem where we assume the divergence function $D$ to be known and we look for a Lagrangian function $\mathfrak{L}$ for which $D$ is a complete solution of the associated Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to replace probability distributions with probability amplitudes.

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Florio M. Ciaglia, Fabio Di Cosmo, Giuseppe Marmo. 2017-11-03. Hamilton-Jacobi Theory and Information Geometry. https://doi.org/10.1007/978-3-319-68445-1_58

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