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Relational Composition of Physical Systems: A Categorical Approach

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arxiv 2310.06088 v1 pith:YXC24NRS submitted 2023-04-01 math.CT math-phmath.MP

Owen Lynch This is my paper · ORCID
classification math.CTmath-phmath.MP
keywords systemsaddressescompositiondevelopframeworkframeworksgeometryphysical
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In this master's thesis, we rigorously develop two frameworks of relational composition of systems using tools from category theory. The first framework addresses port-Hamiltonian systems, which are dynamical systems whose dynamics are connected to flows of energy across a boundary. The second framework addresses thermostatic systems, which are descriptions of equilibria in physical systems using entropy. We also review necessary subjects to develop these frameworks from a category-theoretic viewpoint, including inear algebra, differential geometry, and convex geometry.

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Cited by 1 Pith paper

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  1. Double Categories of Open Systems: the Cospan Approach

    math.CT 2025-09 conditional novelty 4.0 of 10

    Structured and decorated cospan double categories for open systems have an exoskeleton/outer shell structure, and every object in them is a special symmetric Frobenius pseudomonoid.

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