Abstract
Statistical physics revolutionized the understanding of the macroscopic properties of physics by linking them to microscopic interactions. This made it possible to unify separate branches of 19th century physics, such as mechanics, electromagnetics, optics, thermodynamics and chemistry. The lecture begins by describing the historical development of the ideas of statistical physics from Clausius to Boltzmann and Gibbs, through the emergence of the notion of entropy, first in thermodynamics.
A particularly revolutionary aspect of statistical physics is the introduction of probabilistic modeling of macroscopic, apparently deterministic phenomena. The link between deterministic phenomena and probabilistic analysis lies at the heart of high-dimensional data modeling. It results from concentration properties due to the law of large numbers, illustrated in the case of a Gaussian distribution that concentrates on an ellipse in a high-dimensional space. A fundamental challenge in modeling high-dimensional data is to capture the properties of non-Gaussian probability distributions, which reveal, for example, geometric structures in an image, or harmonic components in a sound.
