A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation

It is common lore that the canonical gravitational partition function [Formula: see text] associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up [Formula: see text] diverges. We review here h...

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Detalles Bibliográficos
Autores principales: Pennini, Flavia, Plastino, Angel, Rocca, Mario, Ferri, Gustavo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Review
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515174/
https://www.ncbi.nlm.nih.gov/pubmed/33267391
http://dx.doi.org/10.3390/e21070677
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author Pennini, Flavia
Plastino, Angel
Rocca, Mario
Ferri, Gustavo
author_facet Pennini, Flavia
Plastino, Angel
Rocca, Mario
Ferri, Gustavo
author_sort Pennini, Flavia
collection PubMed
description It is common lore that the canonical gravitational partition function [Formula: see text] associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up [Formula: see text] diverges. We review here how to avoid this pitfall and obtain a (classical) statistical mechanics of Newton’s gravitation. This is done using (1) the analytical extension treatment obtained of Gradshteyn and Rizhik and (2) the well known dimensional regularization technique.
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spelling pubmed-75151742020-11-09 A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation Pennini, Flavia Plastino, Angel Rocca, Mario Ferri, Gustavo Entropy (Basel) Review It is common lore that the canonical gravitational partition function [Formula: see text] associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up [Formula: see text] diverges. We review here how to avoid this pitfall and obtain a (classical) statistical mechanics of Newton’s gravitation. This is done using (1) the analytical extension treatment obtained of Gradshteyn and Rizhik and (2) the well known dimensional regularization technique. MDPI 2019-07-11 /pmc/articles/PMC7515174/ /pubmed/33267391 http://dx.doi.org/10.3390/e21070677 Text en © 2019 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 Review
Pennini, Flavia
Plastino, Angel
Rocca, Mario
Ferri, Gustavo
A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation
title A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation
title_full A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation
title_fullStr A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation
title_full_unstemmed A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation
title_short A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation
title_sort review of the classical canonical ensemble treatment of newton’s gravitation
topic Review
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515174/
https://www.ncbi.nlm.nih.gov/pubmed/33267391
http://dx.doi.org/10.3390/e21070677
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