Extending Cercignani's conjecture results from Botzmann to Boltzmann-Fermi-Dirac equation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917584649060352 |
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| author | Borsoni, Thomas |
| author_facet | Borsoni, Thomas |
| contents | We establish a connection between the relative Classical entropy and the relative Fermi-Dirac entropy, allowing to transpose, in the context of the Boltzmann or Landau equation, any entropy-entropy production inequality from one case to the other; therefore providing entropy-entropy production inequalities for the Boltzmann-Fermi-Dirac operator, similar to the ones of the Classical Boltzmann operator. We also provide a generalized version of the Csisz{á}r-Kullback-Pinsker inequality to weighted Lp norms, 1 $\le$ p $\le$ 2 and a wide class of entropies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11956 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extending Cercignani's conjecture results from Botzmann to Boltzmann-Fermi-Dirac equation Borsoni, Thomas Analysis of PDEs Mathematical Physics We establish a connection between the relative Classical entropy and the relative Fermi-Dirac entropy, allowing to transpose, in the context of the Boltzmann or Landau equation, any entropy-entropy production inequality from one case to the other; therefore providing entropy-entropy production inequalities for the Boltzmann-Fermi-Dirac operator, similar to the ones of the Classical Boltzmann operator. We also provide a generalized version of the Csisz{á}r-Kullback-Pinsker inequality to weighted Lp norms, 1 $\le$ p $\le$ 2 and a wide class of entropies. |
| title | Extending Cercignani's conjecture results from Botzmann to Boltzmann-Fermi-Dirac equation |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2304.11956 |