Entropy-Smooth Structures on Topological Manifolds
Differential Geometry
2026-01-21 v3 General Topology
Abstract
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.
Cite
@article{arxiv.2512.07660,
title = {Entropy-Smooth Structures on Topological Manifolds},
author = {Amandip Sangha},
journal= {arXiv preprint arXiv:2512.07660},
year = {2026}
}