Abstract
These lecture notes present an introduction to the theory of lattice gas automata using the methods of non-equilibrium statistical mechanics and kinetic theory. The micro-dynamic, Boltzmann and Liouville equation are studied. The importance of the semi-detailed balance condition is that it guarantees universal equilibrium states, which are described by the Gibbs’ distributions of statistical mechanics. The lack of Galilei in-variance introduces the non-Galilean factor, for which an exact third order fluctuation formula is derived. The Navier Stokes equation is obtained by applying a Chapman-Enskog type method to the Liouville equation, which results into a Green Kubo formula for the viscosity. Also included is an explicit evaluation of this formula in the Boltzmann approximation.
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Ernst, M.H. (1992). Statistical Mechanics and Kinetic Theory of Lattice Gas Cellular Automata. In: Mareschal, M., Holian, B.L. (eds) Microscopic Simulations of Complex Hydrodynamic Phenomena. NATO ASI Series, vol 292. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2314-1_12
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DOI: https://doi.org/10.1007/978-1-4899-2314-1_12
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