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Heat transport and diffusion in a canonical model of a relativistic gas

Relativistic transport phenomena are important from both theoretical and practical point of view. Accordingly, hydrodynamics of relativistic gas has been extensively studied theoretically. Here, we introduce a three-dimensional canonical model of hard-sphere relativistic gas which allows us to impose appropriate temperature gradient along a given direction maintaining the system in a non-equilibrium steady state. We use such a numerical laboratory to study the appropriateness of the so-called first order (Chapman-Enskog) relativistic hydrodynamics by calculating various transport coefficients. Our numerical results are consistent with predictions of such a theory for a wide range of temperatures. Our results are somewhat surprising since such linear theories are not consistent with the fundamental assumption of the special theory of relativity ($v\leq c$). We therefore seek to explain such results by studying the appropriateness of diffusive transport in the relativistic gas, comparing our results with that of a classical gas. We find that the relativistic correction (constraint) in the hydrodynamic limit amounts to small negligible corrections, thus indicating the validity of the linear approximation in near equilibrium transport phenomena.