The study of the statistical regularities observed in the field of the information production and use has confirmed the existence of important similarities. Thus, the existence of regularities and measurable ratios allow the prevision and the concept of laws. In the fifties, C. Shannon (Shannon C., Weaver W. 1975 : Théorie mathématique de la communication, Bibliothèque du CELP, 1975) modeled the information circulation theory. The entropy hypothesis of this theory is: the more ranked a system is, the less information it produces. Theoretical studies have tried to formalize the connection between the bibliometric distribution and the entropy. In this paper we try to extend previous results linked with "the least effort principle" and the analytical slope of a bibliometric distribution. In the first and second parts we present some recalls about entropy and bibliometric distributions, and after that, we describe different links between them.