On a generic entropy measure in physics and information

  • Authors:

  • Michel S. Elnaggar;Achim Kempf

  • Affiliations:

  • CALIT2, University of California San Diego, La Jolla, California;Dept. of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada

  • Venue:
  • WiOPT'09 Proceedings of the 7th international conference on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
  • Year:
  • 2009

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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.