Chaotic distributions for relativistic particles

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