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Entropy
Volume 21
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10.3390/e21070677
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Review

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

by
Flavia Pennini
1,2,3,*,
Angel Plastino
2,4,
Mario Rocca
2,4,5 and
Gustavo Ferri
1
1
Fac. de C. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, La Pampa 6300, Argentina
2
Consejo Nacional de Investigaciones Científicas y Tecnológicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina
3
Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta 2340000, Chile
4
Departamento de Física, Universidad Nacional de La Plata, La Plata 1900, Argentina
5
Departamento de Matemática, Universidad Nacional de La Plata, La Plata 1900, Argentina
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(7), 677; https://doi.org/10.3390/e21070677
Submission received: 9 May 2019 / Revised: 5 July 2019 / Accepted: 8 July 2019 / Published: 11 July 2019
(This article belongs to the Special Issue Entropy and Gravitation)
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Abstract

It is common lore that the canonical gravitational partition function Z associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up Z 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.
Keywords: Boltzmann-Gibbs distribution; divergences; dimensional regularization; specific heat Boltzmann-Gibbs distribution; divergences; dimensional regularization; specific heat

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MDPI and ACS Style

Pennini, F.; Plastino, A.; Rocca, M.; Ferri, G. A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation. Entropy 2019, 21, 677. https://doi.org/10.3390/e21070677

AMA Style

Pennini F, Plastino A, Rocca M, Ferri G. A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation. Entropy. 2019; 21(7):677. https://doi.org/10.3390/e21070677

Chicago/Turabian Style

Pennini, Flavia, Angel Plastino, Mario Rocca, and Gustavo Ferri. 2019. "A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation" Entropy 21, no. 7: 677. https://doi.org/10.3390/e21070677

APA Style

Pennini, F., Plastino, A., Rocca, M., & Ferri, G. (2019). A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation. Entropy, 21(7), 677. https://doi.org/10.3390/e21070677

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