Hydrodynamization times of a holographic fluid far from equilibrium

TL;DR

This study examines hydrodynamization times in a strongly coupled plasma undergoing Bjorken flow, revealing a hierarchy in the approach to hydrodynamics and the influence of initial conditions on the process.

Contribution

It provides a detailed comparison of hydrodynamization times across different hydrodynamic frameworks and initial conditions in a holographic plasma.

Findings

Hydrodynamization times are similar for Borel resummed attractor and Navier-Stokes.

Entropy density reaches second-order hydrodynamics before Navier-Stokes regime.

Solutions violating weak energy conditions take longer to hydrodynamize.

Abstract

We investigate several hydrodynamization times for an ensemble of different far-from-equilibrium solutions of the strongly coupled $\mathcal{N}=4$ Supersymmetric Yang-Mills plasma undergoing Bjorken flow. For the ensemble of initial data analyzed in the present work, we find that, with typical tolerances between $3\%$ to $5\%$, the average hydrodynamization time associated with the late time convergence of the pressure anisotropy to the corresponding Borel resummed hydrodynamic attractor is approximately equal to the average hydrodynamization time associated with the Navier-Stokes result, while both are shorter than the average hydrodynamization time associated with second-order hydrodynamics. On the other hand, we find that the entropy density of the different solutions coalesces to second-order hydrodynamics long before entering in the Navier-Stokes regime. A clear hierarchy between the different average hydrodynamization times of the Bjorken expanding fluid is established for the set of analyzed initial data, comprising also some solutions which, whilst satisfying the dominant and the weak energy conditions at the initial time, evolve such as to transiently violate one or both conditions when the fluid is still far from equilibrium. In particular, solutions violating the weak energy condition are generally found to take a longer time to enter in the hydrodynamic regime than the other solutions.