Manifestly covariant classical correlation dynamics II. Transport equations and Hakim equilibrium conjecture

Abstract

This is the second of a series of papers on the special relativistic classical statistical mechanics. Employing the general theory developed in the first paper we rigorously derive the relativistic Vlasov, Landau and Boltzmann equation. The latter two advocate the J{\"u}ttner distribution as the equilibrium distribution. We thus, at the full microscopic level, provide a support for the recent numerical finding [D. Cubero {\it et. al.}, Phys. Rev. Lett. \textbf{99}, 170601 (2007)] of the special relativistic generalization of the Maxwell-Boltzmann distribution. Furthermore, the present theory allows us to rigorously calculate various correlation functions at the relativistic many-body equilibrium. Therefore, the relativistic many-body equilibrium conjecture of Hakim is justified.