稀气体动力学：统计方法
Dynamics of dilute gases: a statistical approach
摘要：
根据观测尺度的不同，气体的演化可以用不同的模型来描述。希尔伯特在他的第六个问题中提出的一个自然问题是，这些模型是否提供了一致的预测。特别是对于稀薄气体，人们期望动力学理论的连续性定律可以直接从由力学基本原理支配的分子动力学中得到。在硬球气体的情况下，兰福德表明，玻尔兹曼方程出现在低密度极限的大数定律，至少在很短的时间。本调查的目的是介绍在理解这一限制过程方面的最新进展，提供完整的统计描述。
英文摘要：
The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied gases, it is expected that continuum laws of kinetic theory can be obtained directly from molecular dynamics governed by the fundamental principles of mechanics. In the case of hard sphere gases, Lanford showed that the Boltzmann equation emerges as the law of large numbers in the low density limit, at least for very short times. The goal of this survey is to present recent progress in the understanding of this limiting process, providing a complete statistical description.
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