  The length dependence of the thermal conductivity over more than two decades
is systematically studied for a range of materials, interatomic potentials and
temperatures, by the atomistic approach-to-equilibrium molecular dynamics
method (AEMD). By comparing the values of conductivity obtained for a given
supercell length and maximum phonon mean-free-path (MFP), we find that such
values are strongly correlated, demonstrating that the AEMD calculation with a
supercell of finite length, actually probes the thermal conductivity
corresponding to a maximum phonon MFP. As a consequence, the less pronounced
length dependence usually observed for poorer thermal conductors, such as
amorphous silica, is physically justified by their shorter average phonon MFP.
Finally, we compare different analytical extrapolations of the conductivity to
infinite length, and demonstrate that the frequently used Matthiessen rule is
not applicable in AEMD. An alternative extrapolation more suitable for
transient-time, finite-supercell simulations is derived. This approximation
scheme can also be used to classify the quality of different interatomic
potential models with respect to their capability of predicting the
experimental thermal conductivity.
