2nd International Workshop on Physics-Inspired Paradigms in Wireless Communications and Networks

Research Article

On a Generic Entropy Measure in Physics and Information

  • @INPROCEEDINGS{10.1109/WIOPT.2009.5291598,
        author={Michel Elnaggar and Achim Kempf},
        title={On a Generic Entropy Measure in Physics and Information},
        proceedings={2nd International Workshop on Physics-Inspired Paradigms in  Wireless Communications and Networks},
        publisher={IEEE},
        proceedings_a={PHYSCOMNET},
        year={2009},
        month={10},
        keywords={dimensionality; information and thermodynamics; l\^{}p norm; R\^{e}nyi entropy; Shannon and R\^{e}nyi axioms},
        doi={10.1109/WIOPT.2009.5291598}
    }
    
  • Michel Elnaggar
    Achim Kempf
    Year: 2009
    On a Generic Entropy Measure in Physics and Information
    PHYSCOMNET
    IEEE
    DOI: 10.1109/WIOPT.2009.5291598
Michel Elnaggar1,*, Achim Kempf2,*
  • 1: CALIT2 University of California San Diego La Jolla, California 92093-0436, USA
  • 2: Dept. of Applied Mathematics University of Waterloo Waterloo, Ontario N2L 3G1, Canada
*Contact email: mselnaggar@ieee.org, akempf@math.uwaterloo.ca

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.