The principle of maximum entropy

There is no need to stress the importance of variational problems in mathematics and its applications. The list of variational problems, of different degrees of difficulty, is very long, and it stretches from famous minimum and maximum problems of antiquity, through the variational problems of analytical mechanics and theoretical physics, all the way to the variational problems of modern opera t ions research. While maximizing or minimizing a function or a functional is a routine procedure, some special variational problems give solutions which either unify previously unconnected results or match surprisingly well the results of our experiments. Such variational problems are called variational principles. Whether or not the architecture of our world is based on variational principles is a philosophical problem. But it is a sound strategy to discover and apply variational principles in order to acquire a better understanding of a part of this architecture. In applied mathematics we get a model by taking into account some connections and, inevitably, ignoring others. One way of making a model convincing and useful is to obtain it as the solution of a variational problem. The aim of the present paper is to bring some arguments in favour of the promotion of the variational problem of entropy maximization to the rank of a variational principle.