Stationarity, ergodicity, and entropy in relativistic systems

¹  Departamento de Física Aplicada I, EUP, Universidad de Sevilla - Calle Virgen de África 7, 41011 Sevilla, Spain, EU
²  Rudolf Peierls Centre for Theoretical Physics, University of Oxford - 1 Keble Road, Oxford OX1 3NP, UK, EU

Corresponding author: dcubero@us.es

Received: 31 March 2009
Accepted: 24 July 2009

Abstract

Recent molecular-dynamics simulations show that a dilute relativistic gas equilibrates to a Jüttner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian motion processes, on the other hand, implies that stationary one-particle distributions can differ depending on the underlying time parameterizations. Using molecular-dynamics simulations, we demonstrate how this relativistic phenomenon can be understood within a deterministic model system. We show that, depending on the time parameterization, one can distinguish different types of “soft” ergodicity on the level of the one-particle distributions. Our analysis further reveals a close connection between time parameters and entropy in special relativity. A combination of different time parameterizations can potentially be useful in simulations that combine molecular-dynamics algorithms with randomized particle creation, annihilation, or decay processes.