The Kac Model and (Non-)Equilibrium Statistical Mechanics

SIAM Student Seminar
Friday, October 4, 2019 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 249
Prof. Federico Bonetto (Distinguished Speaker) – GT Math
Jiaqi Yang

In 1959 Mark Kac introduced a simple 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 the Boltzmann 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 an 
attempt to reintroduce some form of space structure and non-equilibrium 
evolution in a way that preserve the mathematical tractability of the