Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State

TL;DR

This paper develops a relativistic lattice Boltzmann method capable of modeling systems with arbitrary, thermodynamically consistent equations of state, extending beyond ideal gas assumptions.

Contribution

It derives a new Boltzmann-like equation that produces a conserved energy-momentum tensor for arbitrary equations of state and implements a lattice scheme verified for QCD.

Findings

Successfully models QCD in Milne metric

Matches viscous fluid dynamics results

Extends lattice Boltzmann methods to non-ideal equations of state

Abstract

The relativistic Boltzmann equation for a single particle species generally implies a fixed, unchangeable equation of state that corresponds to that of an ideal gas. Real-world systems typically have more complicated equation of state which cannot be described by the Boltzmann equation. The present work derives a 'Boltzmann-like' equation that gives rise to a conserved energy-momentum tensor with an arbitrary (but thermodynamically consistent) equation of state. Using this, a Lattice Boltzmann scheme for diagonal metric tensors and arbitrary equations of state is constructed. The scheme is verified for QCD in the Milne metric by comparing to viscous fluid dynamics.