Comptes Rendus
Newtonian gravity in d dimensions
Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 331-342.

We study the influence of the dimension of space on the thermodynamics of the classical and quantum self-gravitating gas. We consider Hamiltonian systems of self-gravitating particles described by the microcanonical ensemble and self-gravitating Brownian particles described by the canonical ensemble. We present a gallery of caloric curves in different dimensions of space and discuss the nature of phase transitions as a function of the dimension d. We also provide the general form of the Virial theorem in d dimensions and discuss the particularity of the dimension d=4 for Hamiltonian systems and the dimension d=2 for Brownian systems.

J'étudie l'influence de la dimension de l'espace sur la thermodynamique du gaz auto-gravitant classique et quantique. Je considère des systèmes hamiltoniens de particules auto-gravitantes décrits par l'ensemble microcanonique et des systèmes de particules browniennes auto-gravitantes décrits par l'ensemble canonique. Je présente une galerie de courbes caloriques pour différentes dimensions de l'espace et discute la nature des transitions de phase en fonction de la dimension d. Je fournis aussi la forme générale du théorème du Viriel en d dimensions et discute la particularité de la dimension d=4 pour les systèmes hamiltoniens et de la dimension d=2 pour les systèmes browniens.

Published online:
DOI: 10.1016/j.crhy.2006.01.005
Keywords: Newtonian gravity, Self-gravitating gas, Brownian systems
Mots-clés : Gravité newtonienne, Gaz auto-gravitant, Systèmes browniens

Pierre-Henri Chavanis 1

1 Laboratoire de physique théorique, université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse, France
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Pierre-Henri Chavanis. Newtonian gravity in d dimensions. Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 331-342. doi : 10.1016/j.crhy.2006.01.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.01.005/

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