On a generic entropy measure in physics and information

Abstract

We define a generalized entropy that measures the evenness of the distribution of the real non-negative elements of a multiset X . The approach is to determine a comparison multiset R which is in a precise sense equivalent to X and which contains only one distinct positive element, whose multiplicity k then yields the desired measure. To this end, R and X are considered equivalent if their p− and q− norms coincide. Accordingly, we define k and its logarithm to be the effective cardinality and the generalized entropy of X respectively, of the order p,q . We show that the new entropy measure is a generalization of the Rényi entropy after proper normalization of the multiset elements. We also discuss some properties of the proposed measure.