**2.1 Limitations of molecular dynamics**

As any simulation technique, molecular dynamics suffers from some intrinsic limitations. The most obvious is the limitation in system size. This may be critical in the modeling of real scale devices with disparate length scales ranging from 1nm to microns. To address such situations, MD should be coupled with a more mesoscopic method, such as the Boltzmann Transport Equations, where the microscopic information on the phonon lifetime is used as input in a Boltzmann equation.

We have also mentioned that a finite system size cuts the long wavelength phonon modes. As we will see, this affects only mildly the measurement of the thermal conductivity unless we couple the system with heat reservoirs.

The second limitation of MD is its classical nature. Each phonon mode is equally populated, and the heat capacity is given to a good approximation by the Dulong-Petit law. This is a good approximation if one ever considers solids above or just below their Debye temperature. However, many materials do not obey this condition at ambient temperature. Quantum effects in MD may be accounted for in different ways. The phonon lifetimes computed from MD may be used in a Boltzmann transport equation which includes quantum statistics in the phonon occupation number (McGaughey 2004). Quantum effects may be also directly incorporated in the course of a MD simulation, using a Langevin thermostat with a colored noise consistent with a Bose-Einstein distribution for the phonon modes (Dammak2009).

Finally, the electronic degrees of freedom are not explicitly simulated in MD. Hence, it is not possible to probe thermal transport in electrical conductors, and in its basic version the contribution of electron-phonon scattering to the transport in semi-conductors is not accounted for.
