Kinetic Theory beyond the Stosszahlansatz
In a recent paper (Chliamovitch, et al., 2015), we suggested using the principle of maximum entropy to generalize Boltzmann’s Stosszahlansatz to higher-order distribution functions. This conceptual shift of focus allowed us to derive an analog of the Boltzmann equation for the two-particle distribut...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/8/381 |
| _version_ | 1798005015721279488 |
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| author | Gregor Chliamovitch Orestis Malaspinas Bastien Chopard |
| author_facet | Gregor Chliamovitch Orestis Malaspinas Bastien Chopard |
| author_sort | Gregor Chliamovitch |
| collection | DOAJ |
| description | In a recent paper (Chliamovitch, et al., 2015), we suggested using the principle of maximum entropy to generalize Boltzmann’s Stosszahlansatz to higher-order distribution functions. This conceptual shift of focus allowed us to derive an analog of the Boltzmann equation for the two-particle distribution function. While we only briefly mentioned there the possibility of a hydrodynamical treatment, we complete here a crucial step towards this program. We discuss bilocal collisional invariants, from which we deduce the two-particle stationary distribution. This allows for the existence of equilibrium states in which the momenta of particles are correlated, as well as for the existence of a fourth conserved quantity besides mass, momentum and kinetic energy. |
| first_indexed | 2024-04-11T12:32:26Z |
| format | Article |
| id | doaj.art-91dbfeb26e2d441f9bbd4aadf08a71cb |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:32:26Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-91dbfeb26e2d441f9bbd4aadf08a71cb2022-12-22T04:23:43ZengMDPI AGEntropy1099-43002017-07-0119838110.3390/e19080381e19080381Kinetic Theory beyond the StosszahlansatzGregor Chliamovitch0Orestis Malaspinas1Bastien Chopard2Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, SwitzerlandDepartment of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, SwitzerlandDepartment of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, SwitzerlandIn a recent paper (Chliamovitch, et al., 2015), we suggested using the principle of maximum entropy to generalize Boltzmann’s Stosszahlansatz to higher-order distribution functions. This conceptual shift of focus allowed us to derive an analog of the Boltzmann equation for the two-particle distribution function. While we only briefly mentioned there the possibility of a hydrodynamical treatment, we complete here a crucial step towards this program. We discuss bilocal collisional invariants, from which we deduce the two-particle stationary distribution. This allows for the existence of equilibrium states in which the momenta of particles are correlated, as well as for the existence of a fourth conserved quantity besides mass, momentum and kinetic energy.https://www.mdpi.com/1099-4300/19/8/381kinetic theorynon-equilibrium statistical mechanicsmaximum entropy principle |
| spellingShingle | Gregor Chliamovitch Orestis Malaspinas Bastien Chopard Kinetic Theory beyond the Stosszahlansatz Entropy kinetic theory non-equilibrium statistical mechanics maximum entropy principle |
| title | Kinetic Theory beyond the Stosszahlansatz |
| title_full | Kinetic Theory beyond the Stosszahlansatz |
| title_fullStr | Kinetic Theory beyond the Stosszahlansatz |
| title_full_unstemmed | Kinetic Theory beyond the Stosszahlansatz |
| title_short | Kinetic Theory beyond the Stosszahlansatz |
| title_sort | kinetic theory beyond the stosszahlansatz |
| topic | kinetic theory non-equilibrium statistical mechanics maximum entropy principle |
| url | https://www.mdpi.com/1099-4300/19/8/381 |
| work_keys_str_mv | AT gregorchliamovitch kinetictheorybeyondthestosszahlansatz AT orestismalaspinas kinetictheorybeyondthestosszahlansatz AT bastienchopard kinetictheorybeyondthestosszahlansatz |