  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.
