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
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.
