  In this paper we conclusively demonstrate that Density Functional
Perturbation Theory calculations of phonon linewidths are not affected by
overscreening issues. Additionally, we present an exact formula designed to
incorporate nonadiabatic and correlation effects while ensuring the positivity
of the linewidths. Finally, we extend the treatment to nonequilibrium scenarios
and offer a rigorous justification for employing the phononic Boltzmann
equation.
