Peculiarities of some classical variational treatments using the maximum entropy principle

We study some peculiarities of the classical variational treatment that applies Jaynes’ maximum entropy principle. The associated variational treatment is usually called MaxEnt. We deal with it in connection with thermodynamics’ reciprocity relations. Two points of view are adopted: (A) One of them is purely abstract, concerned solely with ascertaining compliance of the variational solutions with the reciprocity relations in which one does not need here to have explicit values for the Lagrange multipliers. The other, (B) is a straightforward variation process in which one explicitly obtains the specific values of these multipliers. We focus on the so called q-entropy because it illustrates a situation in which the above two approaches yield different results. We detect an information loss in extracting the explicit form of the normalization-associated Lagrange multipliers.