Five-phonon collisions drive the phonon gas from partial equilibrium (nonzero chemical potential) to full thermochemical equilibrium, with fugacity rising as t to the 4/5 at early times and exponentially at late times.
Khalatnikov, An Introduction to the Theory of Superfluidity, CRC Press-Taylor & Francis, Boca Raton, 2018 (en)
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Phonon number relaxation in a 3D superfluid with a concave acoustic branch
Five-phonon collisions drive the phonon gas from partial equilibrium (nonzero chemical potential) to full thermochemical equilibrium, with fugacity rising as t to the 4/5 at early times and exponentially at late times.