Organizing Physics with Open Energy-Driven Systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908557189840896 |
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| author | Capucci, Matteo Lynch, Owen Spivak, David I. |
| author_facet | Capucci, Matteo Lynch, Owen Spivak, David I. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Organizing Physics with Open Energy-Driven Systems Capucci, Matteo Lynch, Owen Spivak, David I. Category Theory 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. |
| title | Organizing Physics with Open Energy-Driven Systems |
| topic | Category Theory |
| url | https://arxiv.org/abs/2404.16140 |