Second sound is an entropy and temperature wave. At negligible thermal expansion, it has almost zero net mass flux. Lev Davidovich Landau predicted two sound modes in 1941.[ref]
The Theory of Superfluidity of Helium II by Lev Davidovich Landau. Landau, §8, pp.515–516
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Second sound is a phenomenon observed in certain superfluid materials, notably in liquid helium-4 when it is cooled to temperatures near absolute zero. In these states, the normal laws of thermal conduction change, and heat can propagate as a wave, rather than by conventional conduction. In classical materials, heat is transferred by the diffusion of thermal energy, which can be thought of as a statistical flow of phonons (quanta of vibrational energy) and other excitations.