Discrete entropy

Entropy, under different formulations, is an important parameter in mathematics and physics that remains unrivaled when it comes to measure randomness, uncertainty and the like. This being the case, finding akin concepts in new frameworks where such properties may play a role is more than wishful. In this paper we propose to define an entropy for maps on finite sets (that we call discrete entropy) via the so-called permutation entropy, an alternative approach to measure-theoretic and topological entropy that is especially amenable to the methods of discrete mathematics.