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

Abstract

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.Comment: 8 pages, 5 figures. To appear in Physical Review

Thermodynamics of a morphological transition in a relativistic gas

“…In the classical picture, the Markovian nature of the particle velocity in subsequent collisions leads to a Gaussian probability distribution for a random walk. However, in the relativistic systems, the upper-bound limit to velocity prohibits the Gaussian behavior where memory effects introduced into velocity correlation functions lead to non-Markovian processes [6,14,23]. Clearly, the role of such correlations must become more important as temperature rises, however, whether such correlations play a significant role and/or can be related to the critical behavior described here is an important and non-trivial question which are best addressed by a microscopic approaches such as molecular dynamics.…”

“…One certain area which may provide some physical effects is the transport coefficients in a relativistic fluid which has recently gained some attention [24][25][26]. Particularly, the transport of heat due to particle gradient is negligible in a classical fluid, but becomes considerable in the relativistic limit [14,27]. Thus, the ratio of the transport coefficients which measures the relative share of the two mechanisms for transport (that due to particle gradient divided by that due to temperature gradient) is nearly zero in the classical limit (T ≪ 1) and becomes approximately 1/3 in the extreme relativistic regime (T ≫ 1).…”

Transport coefficients for hard-sphere relativistic gas

“…The inter-particle interactions are purely repulsive, and only occur at center-tocenter distance of 2R, otherwise the particles move in straight lines. The collisions are governed by relativistic energy-momentum conservation laws, assuming that momentum is only transferred in the direction of connecting line between the centers (i.e, elastic head-on collisions) [28,43]. The interaction cross section associated with the hard-sphere model is independent of the energy and of the scattering angle.…”

“…In addition to extended theories, attempts have been made in the context of first-order theories to solve the problems associated with relativistic fluids [23][24][25][26][27]. Recent numerical studies have also shown that linear transport laws and first order theories give a good description of equilibration processes [28] and propagation of fluctuations [29] in hydrodynamic limit. The question is to what extent one can rely on the transport coefficients obtained from linear CE method?…”

Molecular dynamics approach to dissipative relativistic hydrodynamics: Propagation of fluctuations

“…which considering the equation of state of an ideal fluid, P = ρT , is representable in the form of Fourier law, q = −κ∇T , and thus revealing the parabolic nature of the theory [44]. However, it leads to a set of hydrodynamic equations with stable equilibrium in a static background (see next section for more details).…”