# Equilibration and hydrodynamics at strong and weak coupling

## TL;DR

This paper reviews methods for describing the approach to hydrodynamics in quark-gluon plasma at both weak and strong coupling, highlighting recent simulation results and holographic models, and discusses future research directions.

## Contribution

It provides an updated overview of weak and strong coupling techniques for plasma hydrodynamization, including recent simulation and holography results, and suggests future improvements with running coupling effects.

## Key findings

- Thermalization time at weak coupling: ~40(η/s)^{4/3}/T
- Hydrodynamization at strong coupling: ~0.41/T
- Finite coupling corrections extend the hydrodynamization time

## Abstract

We give an updated overview of both weak and strong coupling methods to describe the approach to a plasma described by viscous hydrodynamics, a process now called hydrodynamisation. At weak coupling the very first moments after a heavy ion collision is described by the colour-glass condensate framework, but quickly thereafter the mean free path is long enough for kinetic theory to become applicable. Recent simulations indicate thermalization in a time $t\sim40(\eta/s)^{4/3}/T$ [1], with $T$ the temperature at that time and $\eta/s$ the shear viscosity divided by the entropy density. At (infinitely) strong coupling it is possible to mimic heavy ion collisions by using holography, which leads to a dual description of colliding gravitational shock waves. The plasma formed hydrodynamises within a time of $0.41/T$. A recent extension found corrections to this result for finite values of the coupling, when $\eta/s$ is bigger than the canonical value of $1/4\pi$, which leads to $t\sim(0.41+1.6(\eta/s-1/4\pi))/T$ [2]. Future improvements include the inclusion of the effects of the running coupling constant in QCD.