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

Abstract

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 $f(x|\mu )$ 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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