A modified Bakry-Émery $Γ_2$ criterion inequality and the monotonicity of the Tsallis entropy
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915708391129088 |
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| author | Cai, Xiaohan Wang, Xiaodong |
| author_facet | Cai, Xiaohan Wang, Xiaodong |
| contents | The Bakry-Émery $Γ_2$ criterion inequality provides a method for establishing the logarithmic Sobolev inequality. We prove a one-parameter family of weighted Bakry-Émery $Γ_2$ criterion inequalities which in the limit case yields the improved constant due to Ji \cite{Ji24}. Furthermore, we establish a modified weighted $Γ_2$ criterion inequality which could be interpreted as a monotonicity of the Tsallis entropy under the heat flow and yields a family of sharp Sobolev inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A modified Bakry-Émery $Γ_2$ criterion inequality and the monotonicity of the Tsallis entropy Cai, Xiaohan Wang, Xiaodong Differential Geometry Analysis of PDEs The Bakry-Émery $Γ_2$ criterion inequality provides a method for establishing the logarithmic Sobolev inequality. We prove a one-parameter family of weighted Bakry-Émery $Γ_2$ criterion inequalities which in the limit case yields the improved constant due to Ji \cite{Ji24}. Furthermore, we establish a modified weighted $Γ_2$ criterion inequality which could be interpreted as a monotonicity of the Tsallis entropy under the heat flow and yields a family of sharp Sobolev inequalities. |
| title | A modified Bakry-Émery $Γ_2$ criterion inequality and the monotonicity of the Tsallis entropy |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2512.15525 |