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Lattice Boltzmann methods have been developed as powerful tools for computational fluid dymamics. They were originally derived as an ensemble average of lattice gas simulations. By generalizing the collision operator, however, they were developed in a much more powerful tool. A key advantage for high Reynolds number simulations was achieved by allowing for an overrelaxation process, that has no equivalence in the lattice gas picture. Lattice Boltzmann methods are analysed by using kinetic theory approaches to derive the macroscopic equations, which justifies the choices made in the development of the method. This leaves a large amount of freedom in finetuning these methods, leading to a bewildering variety of lattice Boltzmann flavors. In this talk we show that we can derive an integer lattice gas as a coarsegraining of a Molecular Dynamics simulation. In a sense this lattice gas is the "correct" lattice gas implementation, since it will always mirror the underlying Molecular Dynamics simulation. This approach then gives a fundamental implementation of a lattice gas. We examined the fluctuating properties of this lattice gas and uncovered fluctuations that decay surprisingly slowly as we increase the lengthscale of the imposed lattice.This lattice gas can also be ensemble averaged, to give a fundamentally correct lattice Boltzmann method. We have analyzed the properties of this fundamental lattice Boltzmann approach to find the equilibrium distribution, and have started to analyze the properties of the collision operator. Encouragingly the properties of the equilibrium distribution closely mimic that of standard lattice Boltzmann implementations, and the collision operator shows that overrelaxation can be fundamentally understood as a simple consequence of coarsegraining. If you are interested in meeting with the speaker on Monday or Tuesday, please contact Amanda (asiah@lanl.gov) or Qinjun (qkang@lanl.gov). Host: Qinjun Kang 