Mathematical description of MaxEnt PDF projection

As we have mentioned in Section 2.1, all projected PDFs, that is all members of ${\cal G}(T,g)$, are uniquely determined by $H_0$. Thus, the problem now turns to finding the member of ${\cal G}(T,g)$, which has highest entropy. By applying the MaxEnt optimality criterion, we obtain the unique distribution $G^*({\bf x}; T,g)$.