显协变经典相关动力学I。一般理论
Manifestly covariant classical correlation dynamics I. General theory
摘要：
在这一系列的论文中，我们在狭义相对论的框架内，实质性地扩展了Israel和Kandeau关于非平衡态统计力学的研究。这是第一个致力于一般的数学结构。基于超距作用形式，我们得到了一个单时间Liouville方程。这个方程描述了完全经典多体系统的分布函数的明显协变演化。对于这种全局演化，Bogoliubov函数假设是合理的。特别是，使用Balescu-Wallenborn投影算子的方法，我们发现，完整的多体系统的分布函数是完全由约化的单体分布函数。严格推导出约化的单体分布函数所满足的显协变封闭非线性方程。我们还广泛地讨论了对广义相对论的推广，特别是对自引力系统的应用。
英文摘要：
n this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Basing on the action-at-a-distance formalism we obtain a single-time Liouville equation. This equation describes the manifestly covariant evolution of the distribution function of full classical many-body systems. For such global evolution the Bogoliubov functional assumption is justified. In particular, using the Balescu-Wallenborn projection operator approach we find that the distribution function of full many-body systems is completely determined by the reduced one-body distribution function. A manifestly covariant closed nonlinear equation satisfied by the reduced one-body distribution function is rigorously derived. We also discuss extensively the generalization to the general relativity especially an application to self-gravitating systems.
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