Abstract
Fluid dynamics is traditionally thought to apply only to systems near local equilibrium. In this case, the effective theory of fluid dynamics can be constructed as a gradient series. Recent applications of resurgence suggest that this gradient series diverges, but can be Borel resummed, giving rise to a hydrodynamic attractor solution which is well defined even for large gradients. Arbitrary initial data quickly approaches this attractor via nonhydrodynamic mode decay. This suggests the existence of a new theory of far-from-equilibrium fluid dynamics. In this Letter, the framework of fluid dynamics far from local equilibrium for a conformal system is introduced, and the hydrodynamic attractor solutions for resummed Baier-Romatschke-Son-Starinets-Stephanov theory, kinetic theory in the relaxation time approximation, and strongly coupled N=4 super Yang-Mills theory are identified for a system undergoing Bjorken flow.
Highlights
What is fluid dynamics and what is its regime of applicability? Over the centuries, different answers have been given to this question
The textbook definition of the applicability of fluid dynamics is that the local mean free path should be much smaller than the system size
If that mean free path length is larger than the system size, particles will not experience collisions before leaving the system, invalidating a fluid dynamic description
Summary
In relativistic fluid dynamics’ modern formulation, the phenomenological “mean-free-path” criterion is replaced by the requirement that gradients around some reference configuration (typically local equilibrium) are small when compared to system temperature This gives rise to the notion of fluid dynamics as the effective theory of longwavelength excitations, which can be expressed as a hydrodynamic gradient series. Despite gradients in proton collisions being large, low-order hydrodynamics offers a quantitatively accurate description of experimental flow results [10,11,12] This suggests that the mean-free path criterion for the applicability of fluid dynamics is possibly too strict and should be replaced by the ability to neglect the effect from nonhydrodynamic modes [13].
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