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The approach behind EPHS.jl

Compositionality

EPHS formalizes modularity and hierarchical nesting of systems based on a simple, graphical syntax, using ideas from (applied) category theory.

  • explicit separation of syntax and semantics (as different categories)

  • use of directories as a data structure for hierarchically-organized information

    • directories have the algebraic structure of a monad
    • directory-multicategories essentially are a strictification of symmetric monoidal categories
    • idea: combine objects (system interfaces and systems) and morphisms (interconnection patterns and composite systems) in parallel, using human-friendly names instead of a binary monoidal product (i.e. a bifunctor that has to satisfy coherence diagrams)

While the jargon of category theory is likely not attractive to users, designing a compositional framework with these ideas in mind helps to arrive at an ultimately quite simple setup.

Thermodynamic modeling

Whenever the hierarchy of nested subsystems is (made) flat, the remaining subsystems are primitive components. Inspired by the metriplectic or GENERIC framework, the relations that define (the behavior of) the components have a structure that implies a thermodynamically consistent reversible-irreversible splitting. It follows that the first law and second law hold for arbitrarily composed EPHS models. In the jargon of port-Hamiltonian systems, this is achieved first and foremost by replacing the energy storage function (or "Hamiltonian") with an exergy storage function (also called available energy), as discussed in more detail in the first EPHS paper.

Expressions in the graphical syntax (interconnection patterns) can be directly interpreted as energy/exergy flow diagrams, as used in (engineering) thermodynamics (or "thermodynamic optimization" or "exergy analysis").