THE THERMODYNAMICS OF FRACTALS

Introduction. Statistical mechanics, as developed by J.W.Gibbs in the last century, is a theory of great beauty and coherence. By basing it on the concept of ensembles Gibbs freed the theory from the ambiguities related to the introduction of probabilities in deterministic systems, and, at the same time, he created a framework which lends itself easily to gen­ eralizations most importantly the subsequent development of quantum statistical mechanics. The advantage of statistical mechanics over many other fields of science is that the number of degrees of freedom is usually enormously large. This means that the "law of large numbers" singles out certain members of the ensemble as "typical" for given external conditions, and their properties are then described by thermodynamical functions which contain most of the relevant information about macroscopic systems.