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

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...

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Detalles Bibliográficos
Autores principales: Pennini, Flavia, Plastino, Ángel Luis, Rocca, Mario Carlos, Ferri, Gustavo Luis
Formato: Articulo
Lenguaje:Inglés
Publicado: 2019
Materias:
Ciencias Exactas
Boltzmann-Gibbs distribution
Dimensional regularization
Divergences
Specific heat
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/123409
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
Descripción
Sumario: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.

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