Chaotic distributions for relativistic particles

Journal article, 2016

We study a modified Kac model where the classical kinetic energy is replaced by an arbitrary energy function φ(v), v ∈ ℝ. The aim of this paper is to show that the uniform density with respect to the microcanonical measure is Ce-z0φ(v)-chaotic, C, z0 ∈ ℝ+. The kinetic energy for relativistic particles is a special case. A generalization to the case v ∈ ℝd which involves conservation momentum is also formally discussed.