Molecular dynamics approach to dissipative relativistic hydrodynamics: Propagation of fluctuations

Abstract

Relativistic generalization of hydrodynamic theory has attracted much attention from a theoretical point of view. However, it has many important practical applications in high energy as well as astrophysical contexts. Despite various attempts to formulate relativistic hydrodynamics, no definitive consensus has been achieved. In this work, we propose to test the predictions of four types of first-order hydrodynamic theories for non-perfect fluids in the light of numerically exact molecular dynamics simulations of a fully relativistic particle system in the low density regime. In this regard, we study the propagation of density, velocity and heat fluctuations in a wide range of temperatures using extensive simulations and compare them to the corresponding analytic expressions we obtain for each of the proposed theories. As expected in the low temperature classical regime all theories give the same results consistent with the numerics. In the high temperature extremely relativistic regime, not all considered theories are distinguishable from one another. However, in the intermediate regime, a meaningful distinction exists in the predictions of various theories considered here. We find that the predictions of the recent formulation due to Tsumura-Kunihiro-Ohnishi are more consistent with our numerical results than the traditional theories due to Meixner, modified Eckart and modified Marle-Stewart.

Transport coefficients for hard-sphere relativistic gas

“…Another interesting result is that thermal conductivity, in contrast to the other two coefficients, shows a very good agreement with CE theory in the whole range of temperature parameters (less than 3 percent deviation). Such a difference is also observed between propagation of thermal and acoustic modes (which are respectively controlled by thermal conductivity and shear viscosity) in a relativistic fluid [29]. These evidences in addition to the fact that relativistic effects in thermal conductivity emerges at higher temperatures compared to D and η (Fig.…”

“…The model presented above, is a fully relativistic one without adjustable parameters or probabilistic factors that can be employed as a reliable numerical laboratory. So far, it has been successfully used to investigate thermostatistical [28,43] and hydrodynamic [29] properties of relativistic fluids in low density regime. In this work we tend to obtain the transport coefficients using Einstein-Helfand relations and compare simulation results to theoretical predictions based on Chapman-Enskog method.…”

“…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?…”