### How hot can a heat bath get?

Martin Hairer

Abstract:
We consider one of the simplest possible models of non-equilibrium
statistical mechanics: two coupled oscillators in contact with
two Langevin heat baths. The twist is that one of the heat baths
is at "infinite" temperature in the sense that no friction acts
on the corresponding degree of freedom. We explore the question
of the existence of a stationary state in this situation and what
it looks like if it exists. In particular, we will see that the
question "Is the corresponding degree of freedom at infinite
temperature?" can have a surprising variety of answers.