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.