# Contact geometric description of distributed-parameter port-Hamiltonian systems with respect to Stokes-Dirac structures and its information geometry

## TL;DR

This paper presents a geometric framework using contact geometry to describe distributed-parameter port-Hamiltonian systems on Riemannian manifolds, linking energy functionals, Stokes-Dirac structures, and information geometry.

## Contribution

It introduces a contact geometric formulation of distributed-parameter port-Hamiltonian systems and explores the associated information geometry for quadratic energy functionals.

## Key findings

- Distributed-parameter systems are expressed as contact Hamiltonian vector fields.
- Fiber spaces are contact manifolds, base spaces are Riemannian manifolds.
- Information geometry is induced from contact structures and convex energy functionals.

## Abstract

This paper studies distributed-parameter systems on Riemannian manifolds with respect to Stokes-Dirac structures in a language of contact geometry with fiber bundles. For the class where energy functionals are quadratic, it is shown that distributed-parameter port-Hamiltonian systems with respect to Stokes-Dirac structures on one, two, and three dimensional Riemannian manifolds are written in terms of contact Hamiltonian vector fields on bundles. Their fiber spaces are contact manifolds and base spaces are Riemannian manifolds. In addition, for a class of distributed-parameter port-Hamiltonian systems, information geometry induced from contact manifolds and convex energy functionals is introduced and briefly discussed.