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

Pennini, Flavia; Plastino, Angel; Rocca, Mario; Ferri, Gustavo

doi:10.3390/e21070677

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

Flavia Pennini
(
- U.Nat., La Pampa and
- La Plata U. and
- Antofagasta U.
)
,
Angel Plastino
(
- La Plata U.
)
,
Mario Rocca
(
- La Plata U.
)
,
Gustavo Ferri
(
- U.Nat., La Pampa
)

Jul 11, 2019

17 pages

Published in:

Entropy 21 (2019) 7, 677

Published: Jul 11, 2019

DOI:

10.3390/e21070677

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Citations per year

Abstract: (MDPI)

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.

Boltzmann-Gibbs distribution
divergences
dimensional regularization
specific heat
regularization: dimensional
gravitation: partition function
statistical mechanics
specific heat
gravitation: model

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Figures(0)

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