It is common for people who see a R-H vortex tube to remark "Oh how cute,
it's a Maxwell demon".
Uhhh, I don't think so. For starters, it is connected to a huge source of
high-energy air. That is categorically different from the Maxwell demon setup.
Consider the following analogy. We have two black boxes, one of which
contains a R-H vortex tube, the other of which contains an "air cycle
machine" with the following features:
a) We take in high-pressure air at room temperature.
b) We divide the stream. Most if it (95%) we expand adiabatically, by
letting it do work against a turbine. It gets quite cold.
c) The energy that gets dumped into the turbine is transmitted by a shaft
to a disk brake, which gets quite hot.
d) We take the other 5% of the stream and blow it over the brake disk to
keep it from overheating. The air gets quite hot.
e) We summarize the output of this machine by saying there is a cold output
stream and a hot output stream. Just like a R-H vortex tube.
Conclusion: the R-H black box is the same as the air-cycle-machine black
box, except that the latter works better.
The thermodynamics of the R-H tube is not mysterious. The only cute thing
about the R-H tube is that it does the job using fluid dynamics instead of
moving parts.
Note that I did not invent the name "air cycle machine". Machines of this
ilk (with a few additional features) are used on jet aircraft to produce
hot and cold air for the cabin.