摘要翻译：
我们讨论了在维数为$d$的空间中自引力费米子系统的统计力学。我们绘制了自引力费米气体的热量曲线，给出了温度与能量的函数关系，并研究了相变与空间维数的函数关系。我们考虑稳定态（全局熵极大值）和亚稳态（局部熵极大值）。我们证明了对于$D\Ge4$，存在一个临界温度（对于足够大的系统）和一个临界能量，低于这个临界温度的系统不能处于统计平衡。因此，对于$D\GE4$，量子力学不能稳定物质对抗引力坍缩。这与Ehrenfest(1917)在原子水平上发现的库仑力的结果相似。这使得我们宇宙的维度d=3非常特别，可能涉及人择原理。我们的研究进入了研究空间维度如何影响物理定律的科学和哲学论文的悠久传统。
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英文标题：
《Statistical mechanics and thermodynamic limit of self-gravitating
  fermions in D dimensions》
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作者：
Pierre-Henri Chavanis
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  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 $D\ge 4$, 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 $D\ge 4$, quantum mechanics cannot stabilize matter against gravitational collapse. This is similar to a result found by Ehrenfest (1917) at the atomic level for Coulombian forces. This makes the dimension D=3 of our universe very particular with possible implications regarding the anthropic principle. Our study enters in a long tradition of scientific and philosophical papers who studied how the dimension of space affects the laws of physics.
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PDF链接：
https://arxiv.org/pdf/708.1888