Venue
Aula Seminari
Abstract
In 1955 Mark Kac introduced a simplified model for the evolution of a gas of hard spheres undergoing elastic collisions. The main simplification consisted in replacing deterministic collisions with random Poisson distributed collisions.
It is possible to obtain many interesting results for this simplified dynamics, like estimates on the rate of convergence to equilibrium and validity of a Boltzmann type equation. The price paid is that this system has no space structure.
I will review some classical results on the Kac model and report on new results on extensions of the original model via the interaction with one ore more thermostats or heat reservoirs. This is part of a long time program in collaboration with M. Loss to reintroduce to this simple model some form of space structure and non-equilibrium evolution in a way that preserve the mathematical its tractability.