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I have heard several times of the concept of "thermal superconductivity" (As opposed to "electrical superconductivity"), but I am unclear on exactly what that could mean. It turns out to be really hard to google, since everything comes up with thermal effects on electrical superconductivity (critical temperature and all that).

So, given that electrical superconductivity is when electrical current can flow without energy loss, what exactly is the corresponding concept for thermal superconductivity? Given that flows of heat are, well, already composed entirely of heat, what energy-loss mechanism is there that could be minimized? Or am I just completely missing the point?

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Pro tip: quotes are your friends when it comes to google searches: this gives a number of leads – alemi Aug 13 '14 at 18:23
up vote 9 down vote accepted

This is a very interesting question. In fact liquid helium-4 exhibits this property of "thermal superconductivity". What happens is that when one tries to establish a thermal gradient a "temperature wave", also referred to as second sound, propagates. This gives it effectively an infinite thermal conductivity or as you put it, thermal superconductivity. My guess is that you were just calling the phenomenon by unfamiliar names which is why you didn't get a hit online.

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Another technical name of the helium-4 transition is "second sound". – alemi Aug 13 '14 at 23:06
In light of your characterization, would it be fair to say superconductivity is the prevention of gradients from building up, rather than the prevention of losses in flows? That is, it is only coincidental that nonzero electrical gradients imply nonzero ohmic losses? – Chris White Aug 13 '14 at 23:11

In the less exotic world, I understand that single crystals of sapphire of sufficient purity can allow phonons (quanta of sound in a solid) to travel with little or no scattering. Phonons carry energy, and they are the main mechanism of thermal conductivity in solids. This means that heat applied one side of the crystal can travel unimpeded at the speed of sound (very high in sapphire) to the other side.

This "ballistic conduction" of heat via phonons could be considered a form of "thermal superconductivity". Alas it would not in practice allow a persistent current of heat analogous to the persistent current in a superconducting magnet.

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