Entropy and Fisher information in non-convex domains: one chain to rule them all
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912751780102144 |
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| author | Casteras, Jean-Baptiste Flaim, Marco Monsaingeon, Léonard |
| author_facet | Casteras, Jean-Baptiste Flaim, Marco Monsaingeon, Léonard |
| contents | We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the literature by allowing one to completely dispense from $λ$-displacement convexity arguments. Along the way we establish a novel quantitative short-time control of the Fisher information along the Neumann heat flow, and establish an exact chain rule under stronger $AC_2$ assumptions typically satisfied by curves of measures obtained as limits of JKO schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropy and Fisher information in non-convex domains: one chain to rule them all Casteras, Jean-Baptiste Flaim, Marco Monsaingeon, Léonard Analysis of PDEs We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the literature by allowing one to completely dispense from $λ$-displacement convexity arguments. Along the way we establish a novel quantitative short-time control of the Fisher information along the Neumann heat flow, and establish an exact chain rule under stronger $AC_2$ assumptions typically satisfied by curves of measures obtained as limits of JKO schemes. |
| title | Entropy and Fisher information in non-convex domains: one chain to rule them all |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.05826 |