  The predictive modeling of lattice thermal conductivity is of fundamental
importance for the understanding and design of materials for a wide range of
applications. Two major approaches, namely molecular dynamics (MD) simulations
and calculations solving approximately the Boltzmann transport equation (BTE),
have been developed to compute the lattice thermal conductivity. We present a
detailed direct comparison of these two approaches, using as prototypical cases
MgO and PbTe. The comparison, carried out using empirical potentials, takes
into account the effects of fourth order phonon scattering,
temperature-dependent phonon frequencies (phonon renormalization), and
investigates the effects of quantum vs. classical statistics. We clarify that
equipartition, as opposed to Maxwell Boltzmann, govern the statistics of
phonons in MD simulations. We find that lattice thermal conductivity values
from MD and BTE show an apparent, satisfactory agreement; however such an
agreement is the result of error cancellations. We also show that the primary
effect of statistics on thermal conductivity is via the scattering rate
dependence on phonon populations.
