PMID: 15244686Jul 13, 2004Paper

Statistical mechanics and thermodynamic limit of self-gravitating fermions in D dimensions

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
P H Chavanis

Abstract

We discuss the statistical mechanics of a system of self-gravitating fermions in a space of dimension D. We plot the caloric curves of the self-gravitating Fermi gas giving the temperature as a function of energy and investigate the nature of phase transitions as a function of the dimension of space. We consider stable states (global entropy maxima) as well as metastable states (local entropy maxima). We show that for D> or =4, there exists a critical temperature (for sufficiently large systems) and a critical energy below which the system cannot be found in statistical equilibrium. Therefore, for D> or =4, quantum mechanics cannot stabilize matter against gravitational collapse. This is similar to a result found by Ehrenfest (1917) at the atomic level for Coulomb forces. This makes the dimension D=3 of our Universe very particular with possible implications regarding the anthropic principle. Our study joins a long tradition of scientific and philosophical papers that examined how the dimension of space affects the laws of physics.

References

Jun 13, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pierre-Henri Chavanis
Oct 9, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P H Chavanis, I Ispolatov
Nov 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Clément Sire, Pierre-Henri Chavanis
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pierre-Henri Chavanis
Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pierre-Henri Chavanis, Clément Sire

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Citations

Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pierre-Henri Chavanis, Clément Sire
Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pierre-Henri Chavanis, Clément Sire
Jul 7, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F StanisciaG De Ninno
Aug 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Michael Joyce, Tirawut Worrakitpoonpon
Nov 9, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pierre-Henri Chavanis
May 16, 2018·Physical Review. E·Benaoumeur BakhtiGerhard Müller

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