Relativistic third-order viscous corrections to the entropy four-current from kinetic theory

TL;DR

This paper derives a third-order relativistic viscous correction to the entropy four-current using Chapman-Enskog expansion, revealing a non-zero entropy flux and improving agreement with exact Boltzmann solutions.

Contribution

It introduces a new third-order entropy four-current expression with non-vanishing flux, enhancing the accuracy of relativistic hydrodynamics models compared to Grad's method.

Findings

Third-order entropy flux is non-zero, unlike previous models.

Third-order evolution equations align better with Boltzmann and BAMPS results.

Higher-order corrections improve modeling of relativistic fluid dynamics.

Abstract

By employing a Chapman-Enskog like iterative solution of the Boltzmann equation in relaxation-time approximation, we derive a new expression for the entropy four-current up to third order in gradient expansion. We show that unlike second-order and third-order entropy four-current obtained using Grad's method, there is a non-vanishing entropy flux in the present third-order expression. We further quantify the effect of the higher-order entropy density in the case of boost-invariant one-dimensional longitudinal expansion of a system. We demonstrate that the results obtained using third-order evolution equation for shear stress tensor, derived by employing the method of Chapman-Enskog expansion, show better agreement with the exact solution of the Boltzmann equation as well as with the parton cascade BAMPS, as compared to those obtained using the third-order equations from the method of Grad's 14-moment approximation.