Investigating quantum thermodynamics is a killer application for ultracold atoms. From this point of view it is natural to consider tunneling as a peculiarly quantum analog to the Joule-Kelvin throttle, which allows particles, energy, and entropy to pass from one volume to another, at a widely tunable rate that can be made either faster or slower than collisions. I will discuss three simple theoretical calculations that look at tunneling thermodynamically: 'second Josephson oscillations', which are to ordinary Josephson oscillations as second sound is to zero sound in superfluid helium; heat flow in a Bose-Hubbard system coupled to thermal reservoirs of different temperature at opposite; and the fundamental rate at which entropy is generated if tunneling is regarded as an irreversible process.