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.
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Debbasch, F., Mallick, K. & Rivet, J.P. Relativistic Ornstein–Uhlenbeck Process. Journal of Statistical Physics 88, 945–966 (1997). https://doi.org/10.1023/B:JOSS.0000015180.16261.53
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DOI: https://doi.org/10.1023/B:JOSS.0000015180.16261.53