Subject: Shannon-Weaver entropy

From: Minhhuy Ho <[email-masked]>
Date: Thu, 12 Jan 95 13:30:50 EST

Dear Dr. Delaney,

The Shannon-Weaver information entropy measures the uncertainty of 'information'
of a system with continuous probability distribution rho(x) by the relationship

    /
S = | rho(x) ln rho(x) d(x)
    /

There have been several attempts to apply the Shannon entropy to elucidate
chemical and physical properties of atomic and molecular systems by our
group and others. The Kullback information entropy distance which is based on
the Shannon-Weaver entropy is calculated as

         /                               /
Id(AB) = | rho_A ln (rho_A/rho_B) d(x) + | rho_B ln (rho_B/rho_A) d(x)
         /                               /

We have investigated the applicability of this distance as a measure of
chemical 'diversity'. Note that rho_A and rho_B in the above equation
indicates that the distance is a relative quantity, as you mentioned in your
post. Following are some articles could be of interested to you:

C. E. Shannon Bell Syst. Tech. J. v27, pp379 (1948)
S. Kullback, Information Theory and Staticstics, Wiley, New York (1959)
S. R. Gadre et al. Phys. Rev. vA 32, pp2602 (1985)
V. H. Smith, Jr. et al. J. Phys. B, v27, pp5149 (1994)
ibid Chem. Phys. Lett., v219, pp15 (1994)
ibid Int. J. Quant. Chem., to be appeared in (1995)

If we can be of any further help, please do not hestitate to contact us. 

Regards,

Minhhuy Ho
Dept. of Chemistry
Queen's University Kingston, ON. Canada
email: [email-masked]
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A good source of information on diversity is any under-graduate book on
ecology. Ecologists have a great deal of experience in studying species
diversity and seem to have developed many methods for quantifying it.

John Delaney
Zeneca Agrochem
[email-masked]