From kinetic theory to dissipative fluid dynamics

TL;DR

The paper addresses how to obtain a causal, stable relativistic dissipative hydrodynamics framework from kinetic theory by deriving the Israel-Stewart equations from the Boltzmann equation using Grad's 14-moment expansion, keeping terms up to second order in the Knudsen number $K$. The authors show that, beyond the familiar NS terms, additional second-order contributions arise, with coefficients that depend on the chosen reference frame, and they demonstrate that the full IS equations apply to non-conformal systems with net charge density. These results extend previous IS and Muronga treatments by including new second-order terms and clarifying their kinetic-theory origin, laying groundwork for accurate, frame-dependent simulations of heavy-ion collision dynamics. The work enables more reliable phenomenology and motivates future multi-species generalizations and numerical implementations for realistic modeling of relativistic fluids.

Abstract

We present the results of deriving the Israel-Stewart equations of relativistic dissipative fluid dynamics from kinetic theory via Grad's 14-moment expansion. Working consistently to second order in the Knudsen number, these equations contain several new terms which are absent in previous treatments.