Variational derivation of the homogeneous Boltzmann equation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911575934238720 |
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| author | Basile, Giada Benedetto, Dario Orrieri, Carlo |
| author_facet | Basile, Giada Benedetto, Dario Orrieri, Carlo |
| contents | We introduce a variational formulation of the homogeneous Boltzmann equation, with hard-sphere cross section, which selects the unique energy conserving solution. We prove that this solution arises from the microscopic dynamics, namely Kac's walk, and we establish the propagation in time of entropic chaoticity, under the minimal assumption that the initial distribution is entropically chaotic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06919 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variational derivation of the homogeneous Boltzmann equation Basile, Giada Benedetto, Dario Orrieri, Carlo Mathematical Physics Probability 35Q20, 82C40 We introduce a variational formulation of the homogeneous Boltzmann equation, with hard-sphere cross section, which selects the unique energy conserving solution. We prove that this solution arises from the microscopic dynamics, namely Kac's walk, and we establish the propagation in time of entropic chaoticity, under the minimal assumption that the initial distribution is entropically chaotic. |
| title | Variational derivation of the homogeneous Boltzmann equation |
| topic | Mathematical Physics Probability 35Q20, 82C40 |
| url | https://arxiv.org/abs/2604.06919 |