A Lorentz invariant thermal lattice gas model

In current lattice gas models particles are constrained to travel along the principal lattice directions between sites, and must advance from one site to another at each time-step. The collision rules are therefore restricted to redistributing momentum along these principal lattice directions. We introduce a computational technique that does not suffer from these limitations. We associate with each particle a continuous momentum, which is used to control the motion of the particle on the lattice. This motion is probabilistic, a quasi-random walk, so after many time-steps the particle's average motion is a straight line. The collision rules are no longer constrained by the lattice and can be more realistically implemented; here we use Lorentz invariant binary elastic collisions. We show that the equilibrium distribution of our model is the relativistic Boltzmann distribution which permits us to find the temperature of the lattice gas.