Statistical hydrodynamics of lattice-gas automata

Abstract

We investigate the space and time behavior of spontaneous thermohydrodynamic fluctuations in a simple fluid modeled by a lattice-gas automaton and develop the statistical-mechanical theory of thermal lattice gases to compute the dynamical structure factor, i.e., the power spectrum of the density correlation function. A comparative analysis of the theoretical predictions with our lattice gas simulations is presented. The main results are (i) the spectral function of the lattice-gas fluctuations is fully compatible with the spectrum obtained from experimental measurements performed in real fluids; (ii) in the long-wavelength limit, the correlations of lattice-gas fluctuations are well described by the Landau-Placzek theory; (iii) at short wavelengths and/or at low densities, good agreement is obtained between the lattice-gas simulation results and the Boltzmann theory. These results provide solid support to the validity of the thermal-lattice-gas automaton as a consistent model system for real fluids.