Emergence of hydrodynamics in expanding relativistic plasmas

TL;DR

This paper analyzes a set of equations describing the transition from collisionless to hydrodynamic behavior in expanding relativistic plasmas, highlighting the mathematical structure that includes all second order hydrodynamics versions.

Contribution

It demonstrates that Israel-Stewart hydrodynamics' early-time success is due to its mathematical structure, not true hydrodynamic behavior.

Findings

Equations describe transition from collisionless to hydrodynamic regimes.

Israel-Stewart equations mimic collisionless behavior due to their structure.

All second order hydrodynamics versions are encompassed in the equations.

Abstract

I consider a simple set of equations that govern the expansion of boost-invariant plasmas of massless particles. These equations describe the transition from a collisionless regime at early time to hydrodynamics at late time. Their mathematical structure encompasses all versions of second order hydrodynamics. We emphasize that the apparent success of Israel-Stewart hydrodynamics at early time has little to do with ``hydrodynamics'' proper, but rather with a particular feature of Israel-Stewart equations that allows them to effectively mimic the collisionless regime.