Hagop Tossounian: “On molecular chaos and its propagation in Kac’s Model coupled to a thermostat”

In 1956 Mark Kac introduced a probabilistic model of N >> 1 identical particles undergoing pairwise collisions. Together with a method now known as propagation of chaos, he derived a kintetic equation for the velocity distribution of a single particle from the master equation of his N-particle system. This equation resembles Boltzmann’s equation.

 In this talk I plan on introducing Kac’s original method, and describing the role of ther mostats in accelerating the rate of approach to equilibrium in the context of Kac’s model, and how the thermostats model well an interaction of a particle with a heat bath having a large but a finite number of particles.