  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.
