Authors

Markus Lohmayer, Owen Lynch, Sigrid Leyendecker

Abstract

Mathematical modeling of real-world physical systems requires the consistent combination of a multitude of physical laws and phenomenological models. This challenging task can be greatly simplified by hierarchically decomposing systems into ultimately simple components. Moreover, the use of diagrams for expressing the decomposition helps make the process more intuitive and facilitates communication, even with non-experts. As an important requirement, models have to respect fundamental physical laws such as the first and the second law of thermodynamics. While some existing modeling frameworks make such guarantees based on structural properties of their models, they lack a formal graphical syntax. We present a compositional and thermodynamically consistent modeling language with a graphical syntax. In terms of its semantics, we essentially endow port-Hamiltonian systems with additional structural properties and a fixed physical interpretation, ensuring thermodynamic consistency in a manner closely related to the metriplectic or GENERIC formalism. While port-Hamiltonian systems are inspired by graphical modeling with bond graphs, neither the link between the two, nor bond graphs themselves, can be easily formalized. In contrast, our syntax is based on a specialization of the well-studied operad of undirected wiring diagrams. By combining a compositional, graphical syntax with an energy-based, thermodynamic approach, the presented modeling language simplifies the understanding, reuse, and modification of complex physical models.

Keywords

bond graphs, compositionality, generic, metriplectic structure, nonequilibrium thermodynamics, undirected wiring diagrams

Citation

BibTeX

@article{Lohmayer_2026,
  title={{Exergetic Port-Hamiltonian systems modeling language}},
  volume={12},
  ISSN={2405-8440},
  DOI={10.1016/j.heliyon.2025.e44191},
  number={1},
  journal={Heliyon},
  publisher={Elsevier BV},
  author={Lohmayer, Markus and Lynch, Owen and Leyendecker, Sigrid},
  year={2026},
  pages={e44191}
}

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References