# Hamilton-Jacobi Theory and Information Geometry

@inproceedings{Ciaglia2017HamiltonJacobiTA, title={Hamilton-Jacobi Theory and Information Geometry}, author={Florio M. Ciaglia and Fabio Di Cosmo and Giuseppe Marmo}, booktitle={International Conference on Geometric Science of Information}, year={2017} }

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…

## 7 Citations

### Reviewing the geometric Hamilton–Jacobi theory concerning Jacobi and Leibniz identities

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

In this survey, we review the classical Hamilton–Jacobi theory from a geometric point of view in different geometric backgrounds. We propose a Hamilton–Jacobi equation for different geometric…

### Geometric Hamilton–Jacobi theory for systems with external forces

- MathematicsJournal of Mathematical Physics
- 2022

In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems and present some examples.…

### Generalized potential functions in differential geometry and information geometry

- MathematicsInternational Journal of Geometric Methods in Modern Physics
- 2019

Potential functions can be used for generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study whether this…

### Hamilton–Jacobi theory for contact systems: autonomous and non-autonomous for the in time-independent contact Hamiltonian

- Mathematics
- 2022

In this paper we obtain two Hamilton–Jacobi equations for time dependent contact Hamiltonian systems. In these systems there is a dissipation parameter and the fact of obtaining two equations reﬂects…

### Geometric Hamilton-Jacobi theory and integrability for nonholonomic and forced hybrid systems

- Mathematics
- 2022

. A hybrid system is a system whose dynamics are controlled by a mixture of both continuous and discrete transitions. The geometric framework for the Hamilton–Jacobi theory is developed to study this…

### Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems

- Mathematics
- 2022

In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton–Jacobi theory for these systems following two…

### Lagrangian description of Heisenberg and Landau–von Neumann equations of motion

- Physics, Mathematics
- 2020

An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau-von Neumann equation on the manifold of quantum states…

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