3.2 Maximum Entropy Closure

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

$$H(f) = - \langle f \ln f -f \rangle$$ (3.7)

under the constraint that a given set of moments of the distribution function $f$ 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.