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

Abstract

This is the second of a series of papers on special relativistic classical statistical mechanics. Employing the general theory developed in the first paper, we derive rigorously the relativistic Vlasov, Landau, and Boltzmann equations, respectively. The latter two equations advocate the Jüttner distribution as the equilibrium distribution. We thus, at the fully microscopic level, provide support for the recent numerical findings of Cubero and co-workers of the special relativistic generalization of the Maxwell-Boltzmann distribution. Furthermore, the present theory allows us to calculate rigorously various correlation functions at the relativistic many-body equilibrium. Therefore, we demonstrate that the relativistic many-body equilibrium conjecture of Hakim is justified.