A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation
Fac. de C. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, La Pampa 6300, Argentina
Consejo Nacional de Investigaciones Científicas y Tecnológicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina
Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta 2340000, Chile
Departamento de Física, Universidad Nacional de La Plata, La Plata 1900, Argentina
Departamento de Matemática, Universidad Nacional de La Plata, La Plata 1900, Argentina
Author to whom correspondence should be addressed.
Received: 9 May 2019 / Revised: 5 July 2019 / Accepted: 8 July 2019 / Published: 11 July 2019
PDF [329 KB, uploaded 11 July 2019]
It is common lore that the canonical gravitational partition function
associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up
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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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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.
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.
Pennini, Flavia; Plastino, Angel; Rocca, Mario; Ferri, Gustavo. 2019. "A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation." Entropy 21, no. 7: 677.
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