Transport coefficients for hard-sphere relativistic gas

TL;DR

This study uses relativistic molecular dynamics simulations to compute transport coefficients of a hard sphere relativistic gas, comparing results with Chapman-Enskog theory across various temperatures, revealing good agreement at low temperatures and deviations at high temperatures.

Contribution

It provides the first thorough numerical investigation of transport coefficients in a relativistic hard sphere gas and assesses the accuracy of Chapman-Enskog predictions in this regime.

Findings

Simulation data agree with theory at low temperatures.

Deviations increase at high temperatures, except for thermal conductivity.

CE theory's inaccuracy in extremely relativistic cases is observed.

Abstract

Transport coefficients are of crucial importance in theoretical as well as experimental studies. Despite substantial research on classical hard sphere/disk gases in low and high density regimes, a thorough investigation of transport coefficients for massive relativistic systems is missing in the literature. In this work a fully relativistic molecular dynamics simulation is employed to numerically obtain the transport coefficients of a hard sphere relativistic gas based on Helfand-Einstein expressions. The numerical data are then used to check the accuracy of Chapmann-Enskog (CE) predictions in a wide range of temperature. The results indicate that while simulation data in low temperature regime agrees very well with theoretical predictions, it begins to show deviations as temperature rises, except for the thermal conductivity which fits very well to CE theory in the whole range of temperature. Since our simulations are done in low density regimes, where CE approximation is expected to be valid, the observed deviations can be attributed to the inaccuracy of linear CE theory in extremely relativistic cases.