Exergetic Port-Hamiltonian Systems: a compositional, energy-based language for modeling mechanical, electromagnetic, and thermodynamic systems

This thesis introduces a novel, compositional, and thermodynamically consistent modeling language for multiphysical systems, encompassing those governed by the principles of classical mechanics, electromagnetism, and thermodynamics. At its core, the language builds on port-Hamiltonian systems theory. By interpreting the Hamiltonian as an exergy storage function, the inherent passivity of port-Hamiltonian systems is fully reconciled with nonequilibrium thermodynamics. Akin to metriplectic systems and the GENERIC formalism, additional structural properties ensure that both the first and second laws of thermodynamics are guaranteed. Inspired by bond graphs, the modeling language features a simple graphical syntax, which is built upon a specialization of the multicategory of undirected wiring diagrams. The compositional syntax not only enables the hierarchical decomposition of complex systems into simple reusable parts but also facilitates communication among human experts, non-experts, AI language models, and computational tools for simulation, optimization, and control. The structured, energy-based approach promotes systematic enhancement and reusability of models across diverse scientific and engineering domains. To demonstrate the utility of the framework, the thesis examines two advanced applications: First, it is shown that the modeling language can serve as a modular multibody framework. While the mathematical formulation of the primitive subsystems is based on the Lie group of Euclidean isometries, the compositional approach allows users to work with higher-level abstractions, starting with bodies and joints. Second, the thesis considers a series of fluid and plasma models. Specifically, an ideal fluid model is reused as a subsystem of a Navier-Stokes-Fourier model, which in turn is reused as a subsystem of two different plasma models. The hierarchical decomposition reveals how increasingly complex models are built from simpler and ultimately primitive subsystems that represent energy storage as well as reversible and irreversible dynamics. The graphical syntax naturally expresses the interconnection of subsystems through shared energy domains.