Authors

Matteo Capucci, Owen Lynch, David I. Spivak

Abstract

Organizing physics has been a long-standing preoccupation of applied category theory, going back at least to Lawvere. We contribute to this research thread by noticing that Hamiltonian mechanics and gradient descent depend crucially on a consistent choice of transformation – which we call a reaction structure – from the cotangent bundle to the tangent bundle. We then construct a compositional theory of reaction structures. Reaction-based systems offer a different perspective on composition in physics than port-Hamiltonian systems or open classical mechanics, in that reaction-based composition does not create any new constraints that must be solved for algebraically. The technical contributions of this paper are the development of symmetric monoidal categories of open energy-driven systems and open differential equations, and a functor between them, functioning as a”functorial semantics”for reaction structures. This approach echoes what has previously been done for open games and open gradient-based learners, and in fact subsumes the latter. We then illustrate our theory by constructing an n-fold pendulum as a composite of n-many pendula.

Citation

  • Journal: Electronic Proceedings in Theoretical Computer Science
  • Year: 2025
  • Volume: 429
  • Issue:
  • Pages: 287–301
  • Publisher: Open Publishing Association
  • DOI: 10.4204/eptcs.429.16

BibTeX

@article{Capucci_2025,
  title={{Organizing Physics with Open Energy-Driven Systems}},
  volume={429},
  ISSN={2075-2180},
  DOI={10.4204/eptcs.429.16},
  journal={Electronic Proceedings in Theoretical Computer Science},
  publisher={Open Publishing Association},
  author={Capucci, Matteo and Lynch, Owen and Spivak, David I.},
  year={2025},
  pages={287--301}
}

Download the bib file

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