Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of   State
  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. 
Paul Romatschke
gr-qc hep-th nucl-th physics.flu-dyn