Re: entropy

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#10

From: Wolfgang Thumser
Date: Wed, 13 Oct 1999 00:00

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Hi Simon,

if H(X) = H(p1,...,pn) is maximal for some p1,...,pn then necessarily
the n+1 partial derivatives of function
F(p1,...,pn,z) := H(p1,...,pn) + z*(p1+...+pn)
vanish w.r.t. all of its arguments p1,...,pn,z.
Altogether this makes n+1 equations for the n+1 unknowns p1,...,pn,z yielding
p1=...=pn=1/n. (This method is known as the method of Lagrangian multipliers
in n dimensional calculus!)

Regards Wolfgang

--
Wolfgang Thumser
Universit��t Bielefeld
Fachbereich Mathematik
email: thumser@mathematik.uni-bielefeld.de

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From: Wolfgang Thumser <thumser@mathematik.uni-bielefeld.de>
Subject: Re: entropy
Date: 1999/10/13
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