RELATIVISTIC ORNSTEIN-UHLENBECK PROCESS

We wish to shed some Light on the problem of thermodynamic irreversibi lity in the relativistic framework. Therefore, we propose a relativist ic stochastic process based on a generalization of the usual Ornstein- Uhlenbeck process: we introduce a relativistic version of the Langevin equation with a damping term which has the correct Galilean limit. We then deduce relativistic Kramers and Fokker-Planck equations and a fl uctuation-dissipation theorem is derived from them. Finally, numerical simulations are used to check the equilibrium distribution in momentu m space and to investigate diffusion in physical space.