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As I understand it, superfluids cannot sustain temperature gradients; specifically, if a gradient is introduced somewhere on the boundary of the superfluid, a "second sound" thermal wave propagates across through the bulk of the superfluid to bring it to a uniform temperature.

What happens, however, if you force a constant gradient on a superfluid? Say, by immersing a couple of metal contacts in it, one of which is externally heated and the other of which is refrigerated so as to maintain a constant temperature differential between them? Would the superfluid equilibrate to the average temperature of the temperature-forcing contacts?

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