| Summary: | The purpose of this dissertation is to provide a direct microscopic underpinning for lattice Boltzmann (and lattice gas) methods. Lattice gases are idealized discrete models that conserve mass and momentum. These conservation laws imply, through the formalism of kinetic theory, that on a macroscopic scale these methods recover the continuity and Navier-Stokes equations. As part of the kinetic theory approach, an ensemble average of the lattice gas is taken leading to a lattice Boltzmann equation. These lattice Boltzmann equations can be implemented directly leading to the new how ubiquitous lattice Boltzmann methods. In this dissertation we step away from justifying lattice Boltzmann methods and the ability of recovering suitable macroscopic equations. Rather, their correspondence to coarse-grained Molecular Dynamics simulations is examine and can be cast in the form of a lattice gas evolution equation. We call this lattice gas the Molecular Dynamic Lattice Gas (MDLG). We use this MDLG to derive the exact formulation for lattice Boltzmann equilibrium distributions, relaxation parameters, and fluctuating properties.
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