 
Summary: JOURNAL OF COMPUTATIONAL PHYSICS 30, 250258 (1979)
An Algorithm for Finding the Distribution of Maximal Entropy*
N. AGMON,+ Y. ALHASSID,+ AND R. D. LEVINE+
Departtnent of Chekstry ; Massachusetts kstitute of' Technology, Cambridge, Massachusetts 02139
Received October 28, 1977; revised April 2.1,1978
An algorithm for determining the distribution of maximal entropy subject to constraints
is presented. The method provides an alternative to the conventional procedure which
requires the numerical solution of a set of implicit nonlinear equations for the Lagrange
multipliers. Here they are determined by seeking a minimum of a concave function, a
procedure which readily lends itself to computational work. The program also incorporates
two preliminary stages. The first verifies that the constraints are linearly independent and
the second checks that a feasible solution exists.
1. TNTR~DUCTI~N
In applications of probability theory to the physical sciences [l] one is often faced
with the problem of determining a distribution consistent with a given set of average
values. For n distinct states one thus seeks a vector x (components xi , xi > 0,
i = l,..., n), characterized by
$I A,ixi = h, , r = I,..., m. (2)
Here Eq. (1) is the normalization condition and (2) defines b, as the average value
of the property A, , whose magnitude in the ith state is A,$ . Equations (1) and (2)
