| Title: | Hierarchie Poissonova operátoru v nerovnovážné termodynamice A hierarchy of Poisson brackets in non-equilibrium thermodynamics |
| Authors: | Pavelka, Michal Klika, Václav Esen, Og˜ul Grmela, Miroslav |
| Citation: | Physica d-nonlinear phenomena, 2016, roč. 335, č. nov 15 2015, s. 54-69. ISSN 0167-2789. |
| Issue Date: | 2016 |
| Publisher: | Elsevier |
| Document type: | článek article |
| URI: | http://hdl.handle.net/11025/25687 https://www.scopus.com/record/display.uri?origin=resultslist&eid=2-s2.0-84991059640 |
| ISSN: | 0167-2789 |
| Keywords: | Poissonova konzole;hierarchie;projekce;nerovnovážná termodynamika;Lie–Poissonova rovnice |
| Keywords in different language: | Poisson bracket;hierarchy;projection;non-equilibrium thermodynamics;Lie–Poisson equation |
| Abstract: | Reverzibilní vývoj makroskopických a mesoskopických systémů lze popsat pomocí dvou složek: energetického funkcionálu a Poissonova operátoru. Cílem této publikace je objasnit jak lze konstruovat Poissonův operátor a jaké další vlastnosti získáme touto konstrukcí. Poissonův operátor řídící reverzibilní vývoj v jedno-částicové kinetické teorii, kinetická teorie binárních směsí, binární směsi kapalin, klasická nevratná termodynamika a klasická hydrodynamika jsou odvozeny z Liouvillovi rovnice. |
| Abstract in different language: | Reversible evolution of macroscopic and mesoscopic systems can be conveniently constructed from two ingredients: an energy functional and a Poisson bracket. The goal of this paper is to elucidate how the Poisson brackets can be constructed and what additional features we also gain by the construction. In particular, the Poisson brackets governing reversible evolution in one-particle kinetic theory, kinetic theory of binary mixtures, binary fluid mixtures, classical irreversible thermodynamics and classical hydrodynamics are derived from Liouville equation. Although the construction is quite natural, a few examples where it does not work are included (e.g. the BBGKY hierarchy). Finally, a new infinite grandcanonical hierarchy of Poisson brackets is proposed, which leads to Poisson brackets expressing non-local phenomena such as turbulent motion or evolution of polymeric fluids. Eventually, Lie–Poisson structures standing behind some of the brackets are identified. |
| Rights: | Plný text není přístupný. © Elsevier |
| Appears in Collections: | Články / Articles (CTM) OBD |
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