Maximum entropy: E.T.Jaynes and thereabout

Abstract

The maximum entropy principle for determining probabilities is discussed. Jaynes'program concerning inductive inference and the foundations of statistical mechanics is reviewed and taken as a guide for the present paper. Attention is devoted to the historical and philosophical aspects of classical statistical mechanics, such as the assumption of equal a priori probability of microstates. The alleged subjectivity of entropy in connection with information theory and irreversible processes is also discussed. Finally, the paper deals with the birth of quantum statistics with emphasis to statistical dependence and indistinguishability in the Bose-Einstein counting procedure. The conclusions suggest that the way of counting elementary cases as assumed as equiprobable is an empirical hypothesis rather than the result of a rational a priori analysis supported by principles such as that if indifference or maximum entropy.