How hot can a heat bath get?
Martin Hairer

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.