Hamilton-Jacobi approach to potential functions in information geometry
Florio M. Ciaglia, Fabio Di Cosmo, Domenico Felice, Stefano Mancini, Giuseppe Marmo, Juan Manuel Pérez-Pardo · Journal of Mathematical Physics · 2017
The search for a potential function S allowing us to reconstruct a given metric tensor g and a given symmetric covariant tensor T on a manifold M is formulated as the Hamilton-Jacobi problem associated with a canonically defined Lagrangian on TM. 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 are outlined.