What Is the Maximum Entropy Principle? Comments on "Statistical Theory on the Functional Form of Cloud Particle Size Distributions"

The basic idea of the maximum entropy principle is presented in a succinct, self-contained manner. The presentation points out some misunderstandings on this principle by Wu and McFarquhar. Namely, the principle does not suffer from the problem of a lack of invariance by change of the dependent variable; thus, it does not lead to a need to introduce the relative entropy as suggested by Wu and McFarquhar. The principle is valid only with a proper choice of a dependent variable, called a restriction variable, for a distribution. Although different results may be obtained with the other variables obtained by transforming the restriction variable, these results are simply meaningless. A relative entropy may be used instead of a standard entropy. However, the former does not lead to any new results unobtainable by the latter.