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arXiv · 2603.11265

Conduction-Diffusion in N-Dimensional settings as irreversible port-Hamiltonian systems

Luis Mora·Yann Le Gorrec·Hector Ramirez·Denis Matignon
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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.

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Luis Mora, Yann Le Gorrec, Hector Ramirez, Denis Matignon. 2026-03-11. Conduction-Diffusion in N-Dimensional settings as irreversible port-Hamiltonian systems. https://arxiv.org/abs/2603.11265

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