Information and Fluctuations

Abstract

It is hardly necessary to point out that information has become a pillar of modern society. The concept of information made its entry into the exact sciences only relatively recently, since it was formalized in the years 1945–1948 by Shannon in order to tackle the technical problems of communication. In actual fact, it was already implicitly present in the idea of entropy introduced by Boltzmann at the end of the nineteenth century. As we shall see, like the idea of stationarity, entropy does not characterize a particular realization, but rather the whole set of possible realizations. In contrast, Kolmogorov complexity is defined for each realization and we may give an intuitive meaning to the idea of fluctuation or randomness that we would sometimes like to attribute to a series of observations.