Abstract:
In 1956, Mark Kac introduced a stochastic model to derive a Boltzmann-like equation. Like the space-homogeneous Boltzmann’s equation, Kac’s equation is ergodic with centered Gaussians as the unique equilibrium state. In this talk, I will introduce Kac’s model, the thermostat used in [1] to guarantee exponentially fast convergence to equilibrium, and sketch the result in [2] how this infinite thermostat can be approximated by a finite but large reservoir.
References:
[1]Bonetto, F., Loss, M.,Vaidyanathan, R.: J. Stat. Phys. 156(4), 647– 667 (2014)
[2]Bonetto F., Loss, M. Tossounian, H. Vaidyanathan, R. Comm. Math. Phys. 351 (2017)