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Helium II is a superfluid, a quantum mechanical state of matter with strange properties .
The thermal conductivity of helium II is greater than that of any other known substance, a million times that of helium I and hundred of times that of copper. This is because heat conduction occurs via a quantum mechanism.
Second sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the usual mechanism of diffusion. Heat takes the place of pressure in normal sound waves. This leads to very high thermal conductivity. It's known as "second sound" because the wave motion of heat is similar to the propagation of sound in air.
Sound waves are fluctuations in the density of molecules in a substance; second sound waves are fluctuations in the density of phonons. Second sound can be observed in any system in which most phonon-phonon collisions conserve momentum. This occurs in superfluids and in dielectric crystals when Umklapp scattering is small.