The entropy production is not always monotone in the space-homogeneous Boltzmann equation
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911569778049024 |
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| author | Silvestre, Luis |
| author_facet | Silvestre, Luis |
| contents | We show an example of a function and a collision kernel for which the entropy production increases in time when we flow it by the space-homogeneous Boltzmann equation. The collision kernel is not any of the physically motivated kernels that are commonly used in the literature. In this particular setting, our result disproves a conjecture of McKean from 1966. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04861 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The entropy production is not always monotone in the space-homogeneous Boltzmann equation Silvestre, Luis Analysis of PDEs Mathematical Physics 35Q20 We show an example of a function and a collision kernel for which the entropy production increases in time when we flow it by the space-homogeneous Boltzmann equation. The collision kernel is not any of the physically motivated kernels that are commonly used in the literature. In this particular setting, our result disproves a conjecture of McKean from 1966. |
| title | The entropy production is not always monotone in the space-homogeneous Boltzmann equation |
| topic | Analysis of PDEs Mathematical Physics 35Q20 |
| url | https://arxiv.org/abs/2604.04861 |