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

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

It is common lore that the canonical gravitational partition function <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">Z</mi> </semantics> </math> </inline-formula> associated with the classical Boltzman...

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Bibliographic Details
Main Authors: Flavia Pennini, Angel Plastino, Mario Rocca, Gustavo Ferri
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Entropy
Subjects:
Boltzmann-Gibbs distribution
divergences
dimensional regularization
specific heat
Online Access:https://www.mdpi.com/1099-4300/21/7/677
Description
Summary:It is common lore that the canonical gravitational partition function <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">Z</mi> </semantics> </math> </inline-formula> associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">Z</mi> </semantics> </math> </inline-formula> diverges. We review here how to avoid this pitfall and obtain a (classical) statistical mechanics of Newton&#8217;s gravitation. This is done using (1) the analytical extension treatment obtained of Gradshteyn and Rizhik and (2) the well known dimensional regularization technique.
ISSN:1099-4300

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