entropy-maximization procedure

A method of finding the most probable pattern of spatial distribution in a system which is subject to restrictions, that is to say, of making the best estimate of a probability distribution from the limited information available.

Entropy may be seen as a measure of a system's disorder, and maximum entropy is maximum disorder within a system; it is the most probable state within a system subject to constraints, since everything tends to disorder.

The method can be illustrated by looking at a method of calculating commuting flows within a city without investigating each individual's movements. Consider a matrix showing individuals taking a trip along a variety of routes. On a micro-scale, the name of each individual is recorded within each cell of the matrix. The macro-scale shows only the column and row total of the matrix. Most macro-states will correspond to a large number of micro-states, and entropy assesses the number of different micro-states which can correspond to a particular macro-state. Maximum entropy shows the greatest correspondence between macro- and micro-states. The macro-state with the maximum entropy value is the most likely pattern to occur.

The mathematics of all this is complicated, to say the least, but the entropy-maximization procedure is superior to many models—such as the gravity model—because it is not deterministic and can be applied to complex situations. The procedure has not been without its detractors who note that, as in the gravity model, no attention is paid to individual evaluation.