Regime of applicability of Israel-Stewart hydrodynamics

Theories of Relativistic Dissipative Fluid Dynamics

“…Furthermore, as demonstrated in [ 160 ], the approach readily applies to systems with multiple conserved charges. Recently, in [ 162 ], the performance of the fluid-dynamical equations obtained from the DNMR approach (where the terms of second order in the Knudsen number have been neglected) and the IReD approach has been compared in the context of an exactly solvable microscopic model of coupled relaxation-type equations. In this simplified setup, it could be seen that omitting the terms of order can significantly impact the accuracy of the DNMR prescription, while the IReD approach turned out to yield a good approximation of the exact dynamics, even if the slowest microscopic mode did not dominate the dynamics of the system.…”

“…More specifically, while in the DNMR method the relaxation time is given only by the largest eigenvalue of the respective inverse collision matrix, in the IReD method, it consists of a weighted sum of all eigenvalues, with the weights quantifying how relevant a certain eigenmode is to the fluid-dynamical quantity under consideration, cf. [ 162 ].…”