Relativistic Ornstein–Uhlenbeck Process

Abstract

We wish to shed some light on the problem of thermodynamic irreversibility in the relativistic framework. Therefore, we propose a relativistic 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 fluctuation-dissipation theorem is derived from them. Finally, numerical simulations are used to check the equilibrium distribution in momentum space and to investigate diffusion in physical space.