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Using analytical tools from linear response theory, we systematically assessthe accuracy of several microscopic derivations of Israel-Stewart hydrodynamicsnear local equilibrium. This allows us to "rank" the different approaches indecreasing order of accuracy as follows: Inverse Reynolds Dominance (IReD),Denicol-Niemi-Moln\'ar-Rischke (DNMR), second-order gradient expansion, and14-moment approximation. We find that IReD theory is far superior toNavier-Stokes, being very accurate both in the asymptotic regime (i.e., forslow processes) and in the transient regime (i.e., on timescales comparable tothe relaxation time). Also, the high accuracy of DNMR is confirmed, butneglecting second-order terms in the Knudsen number, which would render theequations parabolic, introduces serious systematic errors. Finally, in mostcases, the second-order gradient expansion (a.k.a. non-resummed BRSSS) is foundto be more inaccurate than Navier-Stokes in the transient regime. Overall, thisanalysis shows that Israel-Stewart hydrodynamics is falsifiable, and therelaxation time is observable, shedding new light on the debate on theviability of transient hydrodynamics as a well-defined physical theorydistinguished from Navier-Stokes.

The regime of applicability of Israel-Stewart hydrodynamics