On Calculation of Thermal Conductivity from Einstein Relation in   Equilibrium MD
  In equilibrium molecular dynamics, Einstein relation can be used to calculate the thermal conductivity. This method is equivalent to Green-Kubo relation and it does not require a derivation of an analytical form for the heat current. However, it is not commonly used as Green-Kubo relationship. Its wide use is hindered by the lack of a proper definition for integrated heat current (energy moment) under periodic boundary conditions. In this paper, we developed an appropriate definition for integrated heat current to calculate thermal conductivity of solids under periodic conditions. We applied this method to solid argon and silicon based systems; compared and contrasted with the Green-Kubo approach. 
Alper Kinaci, Justin B. Haskins, and Tahir \c{C}a\u{g}{\i}n
physics.chem-ph cond-mat.mtrl-sci