Phonon Quasimomentum: Why & How?

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Why momentum of phonons called quasimomentum? Is it due to the fact that wavenumber of vibrations confined in a first Brillouin zone, and therefore can not have an arbitrary value as "usual" momentum?
 
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The momentum of phonons isn't called quasimomentum. The true momentum of phonons is 0. While the true momentum is a consequence of translational invariance, quasi- or crystal-momentum is a consequence of the permutational symmetry of the atoms in the underlying crystal. See Ashcroft and Mermin, specifically one of the appendices.
 
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DrDu said:
The momentum of phonons isn't called quasimomentum. The true momentum of phonons is 0. While the true momentum is a consequence of translational invariance, quasi- or crystal-momentum is a consequence of the permutational symmetry of the atoms in the underlying crystal. See Ashcroft and Mermin, specifically one of the appendices.

needed that info thanks
Drdu will there be a gain in entropy of phonons , or heat from the movement of phonons