A new proof of the constructability of local equilibrium ensembles

The variational problem δ(Tr(W log W)) = 0 under the constraints Tr(WAi) = αi, Tr W = 1 is investigated. The problem is uniquely solvable, iff there is a strictly positive W which fulfills the constraints. The solution takes the form of a local equilibrium ensemble. The set of the corresponding intensive parameters λi is uniquely determined iff no constant operator is a linear combination of the Ai. The proof uses arguments from the quantum-theoretical theory of measurement.