The maximum entropy principle yields, for a given set of prior information, a density which contains least additional information in the sense of Shannon. It is obtained by maximizing the entropy
under the constraint that a given set of moments of the distribution function assumes prescribed values [Wu97].
A maximum entropy approach to the closure problem was applied by Levermore [Lev96]. A physical approach based on the maximum entropy principle was initiated by Anile [ARR00] within the framework of extended thermodynamics.