Validity of relativistic hydrodynamics beyond local equilibrium

TL;DR

This paper investigates the limits of relativistic hydrodynamics far from equilibrium by analyzing solutions of Boltzmann equations, revealing its effectiveness due to smooth interpolation between free streaming and collective behavior.

Contribution

It introduces a formal solution framework for relativistic kinetic equations that explains hydrodynamics' success beyond local equilibrium conditions.

Findings

Non-perturbative modes are crucial for causality and divergence understanding.

Hydrodynamics' effectiveness stems from interpolation between free streaming and collective dynamics.

Exact non-equilibrium evolution shares structure with gradient expansion, with modified transport coefficients.

Abstract

We examine the applicability of relativistic hydrodynamics far from equilibrium by constructing formal solutions of the Boltzmann moment equations in the relaxation time approximation. These solutions naturally decompose into a divergent gradient series and exponentially decaying non-perturbative modes that encode initial conditions. The non-perturbative contributions are essential for understanding causality, the divergence of the gradient series, and the unexpected effectiveness of relativistic hydrodynamics far from equilibrium. In the 0+1D Bjorken scenario, we demonstrate that the exact evolution of non-equilibrium terms shares the same structural form as the gradient expansion, differing only through modified transport coefficients that reflect both initial data and free-streaming dynamics. Extending to 3+1D, we find that hydrodynamics remains effective not because the system is close to equilibrium, but because it interpolates smoothly between free streaming and collective behavior. This perspective offers a natural explanation for the remarkable success of hydrodynamics in modeling quark-gluon plasma evolution.