A molecular dynamics approach to dissipative relativistic hydrodynamics: propagation of fluctuations

TL;DR

This study uses molecular dynamics simulations to evaluate and compare different first-order relativistic hydrodynamic theories, finding that the Tsumura-Kunihiro-Ohnishi formulation aligns best with numerical results in the intermediate temperature regime.

Contribution

It provides a numerical validation and comparison of four relativistic hydrodynamic theories, highlighting the superior performance of the Tsumura-Kunihiro-Ohnishi model in certain regimes.

Findings

All theories agree with simulations at low temperatures.

In the high relativistic regime, theories become indistinguishable.

The Tsumura-Kunihiro-Ohnishi theory best matches simulation data in the intermediate regime.

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 \emph{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.