Possibility and Impossibility of the Entropy Balance in Lattice Boltzmann Collisions

We demonstrate that in the space of distributions operated on by lattice Boltzmann methods that there exists a vicinity of the equilibrium where collisions with entropy balance are possible and, at the same time, there exist an area of nonequilibrium distributions where such collisions are impossible. We calculate and graphically represent these areas for some simple entropic equilibria using single relaxation time models. Therefore it is shown that the definition of an entropic LBM is incomplete without a strategy to deal with certain highly nonequilibrium states. Such strategies should be explicitly stated as they may result in the production of additional entropy.