We study a modified Kac model where the classical kinetic energy is replaced by an arbitrary energy function $\phi(v)$, $v \in \mathbb{R}$. The aim of this paper is to show that the uniform density with respect to the microcanonical measure is $Ce^{-z_0\phi(v)}$-chaotic, $C,z_0 \in \mathbb{R}_+$. The kinetic energy for relativistic particles is a special case. A generalization to the case $v\in \mathbb{R}^d$ which involves conservation momentum is also formally discussed.

中文翻译：

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相对论粒子的混沌分布

我们研究了一个修正的 Kac 模型，其中经典动能被任意能量函数 $\phi(v)$, $v \in \mathbb{R}$ 代替。本文的目的是证明关于微正则测度的均匀密度是 $Ce^{-z_0\phi(v)}$-chaotic, $C,z_0 \in \mathbb{R}_+$。相对论粒子的动能是一个特例。还正式讨论了对涉及守恒动量的情况 $v\in \mathbb{R}^d$ 的推广。