Maxwell's demon and data analysis

The second principle of thermodynamics introduces a very important concept: the entropy of a macrosystem made of a very great number of microsystems. One of the aims of this work is to point out how, in data analysis, entropy and information, that Maxwell's demon should have to allow a macroscopic reversible process, are closely related. The measure of the information content of a data set allows the analyst to permanently keep under control the variation of information through the successive steps of data processing. On the other hand, multivariate statistics, and among them the factorial analysis of correspondence, can extract the independent and orthogonal sources of information contained in the experimental data. Through several examples dealing with very different experimental situations (stroboscopic observation of a mechanical stress, time-dependent spectroscopy, quantitative elemental mapping by X-ray radiography) we illustrate the usefulness of data analysis before and during data processing.