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On the Contact Geometry and the Poisson Geometry of the Ideal Gas
We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically, we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard 5-dimensional contact manifold used in the literature. This...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512762/ https://www.ncbi.nlm.nih.gov/pubmed/33265340 http://dx.doi.org/10.3390/e20040247 |
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author | Isidro, J. M. Fernández de Córdoba, P. |
author_facet | Isidro, J. M. Fernández de Córdoba, P. |
author_sort | Isidro, J. M. |
collection | PubMed |
description | We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically, we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard 5-dimensional contact manifold used in the literature. This reflects the fact that the internal energy of the ideal gas depends exclusively on its temperature. We also present a Poisson algebra of thermodynamic operators for a quantum-like description of the classical ideal gas. The central element of this Poisson algebra is proportional to Boltzmann’s constant. A Hilbert space of states is identified and a system of wave equations governing the wavefunction is found. Expectation values for the operators representing pressure, volume and temperature are found to satisfy the classical equations of state. |
format | Online Article Text |
id | pubmed-7512762 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75127622020-11-09 On the Contact Geometry and the Poisson Geometry of the Ideal Gas Isidro, J. M. Fernández de Córdoba, P. Entropy (Basel) Article We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically, we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard 5-dimensional contact manifold used in the literature. This reflects the fact that the internal energy of the ideal gas depends exclusively on its temperature. We also present a Poisson algebra of thermodynamic operators for a quantum-like description of the classical ideal gas. The central element of this Poisson algebra is proportional to Boltzmann’s constant. A Hilbert space of states is identified and a system of wave equations governing the wavefunction is found. Expectation values for the operators representing pressure, volume and temperature are found to satisfy the classical equations of state. MDPI 2018-04-03 /pmc/articles/PMC7512762/ /pubmed/33265340 http://dx.doi.org/10.3390/e20040247 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Isidro, J. M. Fernández de Córdoba, P. On the Contact Geometry and the Poisson Geometry of the Ideal Gas |
title | On the Contact Geometry and the Poisson Geometry of the Ideal Gas |
title_full | On the Contact Geometry and the Poisson Geometry of the Ideal Gas |
title_fullStr | On the Contact Geometry and the Poisson Geometry of the Ideal Gas |
title_full_unstemmed | On the Contact Geometry and the Poisson Geometry of the Ideal Gas |
title_short | On the Contact Geometry and the Poisson Geometry of the Ideal Gas |
title_sort | on the contact geometry and the poisson geometry of the ideal gas |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512762/ https://www.ncbi.nlm.nih.gov/pubmed/33265340 http://dx.doi.org/10.3390/e20040247 |
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