On the derivation of entropy conserving equations for commuting macroobservables

Let Ũ be a local equlibrium ensemble, {Oi} a set of commuting observables and B a linear operator with the following properties: 1.1) Tr(BŨOi)=ddt〈Oi〉, 〈Oi〉=Tr(ŨOi).2.2) These equations are entropy conserving for every Ũ. Then Tr(BŨOi)=0, and hence the Euler equations of fluid dynamics cannot be derived.