 
Summary: Volume 53, rmmber 1 CHEMICAL PHYSICS LETTERS 1 January 1978
AN UPPER BOUND FOR THE ENTROPY
AND ITS APPLICATIONS TO THE MAXIMAL ENTROPY PROBLEM*
Y. ALHASSID, N. ACMON and R.D. LEVINE
Department of PtzJF.&alChemistry_, The Hebrew University, JentsaIenz,Israel
Received 31 August 1977
A variational principle where the Lagrange multipliers of a trial distribution are used as variational parameters is discussed
as an efficient. practical route to the determination of the distribution of maximal entropy.
1. Introduction
The determination of a probability distribution of
maximal entropy is of interest in many areas of physics
and chemistry [ 141. The required maximum is typi
cally subject to stibsidiary conditions ("constraints")
on the distribution. The solution of the constrained
maximum problem is traditionally formulated using
the Lagrange multipiiers procedure [ 1,2.4]. One is
then faced with the need tr, solve implicit, nonlinear,
equations in order to determine the numerical value
of the Lagrange multipliers. Whenever more than two
constraints need be imposed, the numerical problem
