Third-order dissipative hydrodynamics from the entropy principle

TL;DR

This paper derives third-order dissipative hydrodynamic equations from the entropy principle, compares their solutions with BAMPS simulations, and highlights the significance of higher-order corrections in high Knudsen number regimes.

Contribution

It provides a derivation of third-order hydrodynamics from the entropy principle and demonstrates their improved accuracy over Israel-Stewart equations in certain regimes.

Findings

Third-order equations closely match BAMPS results.

Grad's approximation accurately describes transverse spectra.

Higher-order corrections are crucial at large Knudsen numbers.

Abstract

We review the entropy based derivation of third-order hydrodynamic equations and compare their solutions in one-dimensional boost-invariant geometry with calculations by the partonic cascade BAMPS. We demonstrate that Grad's approximation, which underlies the derivation of both Israel-Stewart and third-order equations, describes the transverse spectra from BAMPS with high accuracy. At the same time solutions of third-order equations are much closer to BAMPS results than solutions of Israel-Stewart equations. Introducing a resummation scheme for all higher-oder corrections to one-dimensional hydrodynamic equation we demonstrate the importance of higher-order terms if the Knudsen number is large.