Generalized hydrodynamics and dispersion relations in lattice gases

Spectra or decay rates of spatial fluctuations are calculated from mean-field theory or Boltzmann’s equation for thermal and athermal lattice-gas automata, with the emphasis on long-lived hydrodynamic modes. The spectra provide information on isotropy, existence of spurious conservation laws, and time and length scales of hydrodynamic behavior. Particularly important is the range of validity of generalized hydrodynamics with wave-number-dependent sound speed and transport coefficients. These properties give a quantitative explanation of several existing, but unexplained simulation results on the so-called negative bulk viscosities, and on the strong dispersion in the simulation results on sound damping.