Macroscopic approximation to relativistic kinetic theory from a nonlinear closure

TL;DR

This paper develops a macroscopic relativistic fluid model incorporating a nonequilibrium tensor, derived via a nonlinear closure from kinetic theory, and demonstrates improved accuracy over traditional second order fluid dynamics in matching kinetic solutions.

Contribution

It introduces a novel macroscopic closure based on the Entropy Production Principle for relativistic kinetic theory, enhancing the modeling of nonequilibrium effects.

Findings

The new formalism better matches exact Boltzmann solutions than second order fluid dynamics.

Transport coefficients are calibrated to recover second order fluid behavior in small gradient regimes.

The approach provides a more accurate macroscopic description of relativistic particle systems.

Abstract

We use a macroscopic description of a system of relativistic particles based on adding a nonequilibrium tensor to the usual hydrodynamic variables. The nonequilibrium tensor is linked to relativistic kinetic theory through a nonlinear closure suggested by the Entropy Production Principle; the evolution equation is obtained by the method of moments, and together with energy-momentum conservation closes the system. Transport coefficients are chosen to reproduce second order fluid dynamics if gradients are small. We compare the resulting formalism to exact solutions of Boltzmann's equation in 0+1 dimensions and show that it tracks kinetic theory better than second order fluid dynamics.