Boltzmann equation with a nonlocal collision term and the resultant dissipative fluid dynamics

TL;DR

This paper derives a new relativistic dissipative fluid dynamics framework from the Boltzmann equation with a nonlocal collision term, capturing all second-order terms allowed by symmetry and correcting traditional approaches.

Contribution

It introduces a novel derivation method that includes all symmetry-allowed second-order terms and modifies existing coefficients in relativistic fluid dynamics.

Findings

All second-order terms allowed by symmetry are generated.

Some terms previously missed are now included.

Coefficients of certain terms are significantly altered.

Abstract

Starting with the relativistic Boltzmann equation where the collision term was generalized to include gradients of the phase-space distribution function, we recently presented a new derivation of the equations for the relativistic dissipative fluid dynamics. We compared them with the corresponding equations obtained in the standard Israel-Stewart and related approaches. Our method generates all the second-order terms that are allowed by symmetry, some of which have been missed by the traditional approaches, and the coefficients of other terms are altered. The first-order or Navier-Stokes equation too receives a small correction. Here we outline this work for the general audience.