Entropy-Smooth Structures on Topological Manifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908773995511808 |
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| author | Sangha, Amandip |
| author_facet | Sangha, Amandip |
| contents | We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate functions and reconstructs a smooth atlas directly from the quadratic entropy response. We prove that this entropy-smooth structure is equivalent to the classical smooth structure, stable under perturbations, and compatible with products, submanifolds, immersions, and diffeomorphisms. This establishes smoothness as an information-theoretic phenomenon and forms the foundational layer of a broader program linking entropy, diffusion, and differential geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropy-Smooth Structures on Topological Manifolds Sangha, Amandip Differential Geometry General Topology We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate functions and reconstructs a smooth atlas directly from the quadratic entropy response. We prove that this entropy-smooth structure is equivalent to the classical smooth structure, stable under perturbations, and compatible with products, submanifolds, immersions, and diffeomorphisms. This establishes smoothness as an information-theoretic phenomenon and forms the foundational layer of a broader program linking entropy, diffusion, and differential geometry. |
| title | Entropy-Smooth Structures on Topological Manifolds |
| topic | Differential Geometry General Topology |
| url | https://arxiv.org/abs/2512.07660 |