In the literature one often finds covariant relativistic generalizations of classical non equilibrium statistical equations (Boltzmann, Vlasov, Landau, Fokker-Planck, etc...) but I wonder what is the meaning of the time which is used. As far as I know, one can only write the interaction between two relativistic charged particles by doing the computation in the proper space-time frame of one of the particles. With three relativistic charged particles I am already wondering about how to tackle the problem of proper time, so for N close to a mole...I am lost. Since non-equilibrium statistical mechanics is derived from Hamiltonian mechanics, I can reformulate my question as follows. What is the Hamiltonian of N relativistic interacting charged particles ?