Dissipative Dynamics for Large Interacting Systems

I will review recent results and not so recent open problems concerning
constructions and ergodicity of dissipative dynamics for classical and noncommutative large interacting systems. In particular I will talk about dynamics defined by formally hypoelliptic generators and some generalised Dunkl type extensions, and how to control their long time behaviour (by use of coercive inequalities or generalised gradient type bounds).