A link between the maximum entropy approach and the variational entropy form

The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|μ)$ there is a "universal" relation among the entropy rate and the functions appearing in the constraint. It is shown that the recently proposed variational formulation of the entropic functional can be obtained as a consequence of this relation, that is from the maximum entropy principle. This resolves certain puzzling points appeared in the variational approach.

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