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- W1966943624 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 $Densuremath{geqslant}4$, 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 $Densuremath{geqslant}4$, 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." @default.
- W1966943624 created "2016-06-24" @default.
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- W1966943624 date "2004-06-16" @default.
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- W1966943624 title "Statistical mechanics and thermodynamic limit of self-gravitating fermions in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math>dimensions" @default.
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- W1966943624 doi "https://doi.org/10.1103/physreve.69.066126" @default.
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