Infinite-Dimensional Information Ricci Flow Foundations, Variational Derivation, and Singularity Theory
Fuente:
Zenodo
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Langue: | anglais |
| Publié: |
Zenodo
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866901078384050176 |
|---|---|
| author | li, yuanjian |
| author_facet | li, yuanjian |
| contents | <p>This paper develops a complete and rigorous mathematical foundation for the \emph{information Ricci flow} on the infinite-dimensional manifold of smooth positive probability densities on a compact Riemannian manifold. We construct the Fisher--Rao metric, derive the Levi--Civita connection and geodesic equation by explicit variational calculus, and establish local well-posedness in Sobolev spaces. We then introduce an information entropy functional of Perelman type, compute its first variations with respect to both the metric and the density, and derive the information Ricci flow as a gradient flow. A detailed monotonicity formula is obtained. We define information singularities, information horizons, and an information area law. All derivations are original and presented in full detail, providing a rigorous mathematical basis for the principle ``information is matter''.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19326400 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Infinite-Dimensional Information Ricci Flow Foundations, Variational Derivation, and Singularity Theory li, yuanjian information Ricci flow <p>This paper develops a complete and rigorous mathematical foundation for the \emph{information Ricci flow} on the infinite-dimensional manifold of smooth positive probability densities on a compact Riemannian manifold. We construct the Fisher--Rao metric, derive the Levi--Civita connection and geodesic equation by explicit variational calculus, and establish local well-posedness in Sobolev spaces. We then introduce an information entropy functional of Perelman type, compute its first variations with respect to both the metric and the density, and derive the information Ricci flow as a gradient flow. A detailed monotonicity formula is obtained. We define information singularities, information horizons, and an information area law. All derivations are original and presented in full detail, providing a rigorous mathematical basis for the principle ``information is matter''.</p> |
| title | Infinite-Dimensional Information Ricci Flow Foundations, Variational Derivation, and Singularity Theory |
| topic | information Ricci flow |
| url | https://doi.org/10.5281/zenodo.19326400 |