  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.
