Bottom up lattice Boltzmann: the path from Molecular Dynamics to lattice Boltzmann methods

We show how lattice Boltzmann simulations can be understood as a coarsegraining and averaging of Molecular Dynamics simulations. Typically lattice Boltzmann methods are verified by analyzing the hydrodynamic limit of the method. It is known that this approach is not sufficient for several kinds of application. In contrast out approach allows to bottom up derivation of lattice Boltzmann methods, and gives guidance for the design of lattice Boltzmann (or lattice gas) methods for fluctuating and/or non-ideal systems and gives an alternative path to compare competing collision operators and equilibrium distributions as well as forcing terms currently used and gives a fundamental test of what the correct form of these terms is.