Jaynes & Shannon's Constrained Ignorance and Surprise

Abstract: In this simple article, with possible applications in theoretical and applied physics, we suggest an original way to derive the expression of Shannon's entropy from a purely variational approach,using constraints. Based on the work of Edwin T. Jaynes, our results are not fundamentally new but the context in which they are derived might, however, lead to a remarkably consistent formalism,where the maximum entropy principle appears naturally. After having given a general definition of "ignorance" in this framework, we derive the somehow general expected expression for the entropy using two approaches. In the first, one is biased and has a vague idea of the shape of the entropy function. In the second, we consider the general case, where nothing is a priori known. The merits of both ways of thinking are compared.