Conduction-Diffusion in N-Dimensional settings as irreversible port-Hamiltonian systems
Abstract
This work extends previous 1D irreversible port-Hamiltonian system (IPHS) formulations to boundary-controlled ND distributed parameter systems describing conduction-diffusion fluid phenomena. Within a unified and thermodynamically consistent framework, we show that conduction and diffusion can be represented through a single coherent structure that preserves global energy balance and ensures a correct characterization of entropy production. The resulting formulation provides a foundation for the systematic modeling and control of complex multi-physical processes governed by coupled transport mechanisms in N dimensions. In the longer term, this framework opens the door to structure-preserving numerical schemes capable of enforcing thermodynamic principles directly at the discretized level.
Cite
@article{arxiv.2603.11265,
title = {Conduction-Diffusion in N-Dimensional settings as irreversible port-Hamiltonian systems},
author = {Luis Mora and Yann Le Gorrec and Hector Ramirez and Denis Matignon},
journal= {arXiv preprint arXiv:2603.11265},
year = {2026}
}