Joint Mathematical Physics and Analysis and Probability Theory seminar

Abstract:  In Boltzmann’s time the scientific community had not fully accepted the idea that a gas consists of a very large number of particles, molecules or atoms. The equation that bears his name, which gives a statistical description of positions and velocities of particles in a dilute gas, was recognized as important, but also questioned. How could a reversible dynamical system (the particle system) give rise to an equation that respects the second law of thermodynamics, and so is not reversible? In the talk I will explain how the “validation problem” for the Boltzmann equation, fits into Hilbert’s 6-th problem “to treat in the same manner, by means of axioms, those physical sciences in which mathematics plays an important role …”. I will present the Boltzmann equation and the validation problem, show why it is difficult, and give some elements of its solution.