Sur les principes d’incertitude

Abstract

In this thesis we study the general concept of the uncertainty principle. The latter has its origins in quantum mechanics. It has considerably evolved and an exposition of diverse ramifications that exist nowadays is given. The novelty consists in the consideration of an uncertainty principle in the context of diffusions processes called PGV (probability group velocity). The link with etropy is also given. For completeness, we also give in chapter I an introduction to quantum mechanics and show the Heisenberg’s uncertainty principle. In chapter II we give the classical and non commutative counterpart, including some elements on diffusion and Kolmogorov’s equations.