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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 17, Pages 2847-2854

Shannon entropy: axiomatic characterization and application

1Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India
2Department of Mathematics, Heritage Institute of Technology, Chowbaga Road, Anandapur, Kolkata 700107, India

Received 18 February 2005

Copyright © 2005 C. G. Chakrabarti and Indranil Chakrabarty. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We have presented a new axiomatic derivation of Shannon entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function. We have then modified Shannon entropy to take account of observational uncertainty.The modified entropy reduces, in the limiting case, to the form of Shannon differential entropy. As an application, we have derived the expression for classical entropy of statistical mechanics from the quantized form of the entropy.