Hi Steve,
There are several advantages of the Green-Kubo (GK) method compared to the non-equilibrium method (NEMD). 1) Because GK simulations are done with the system in equilibrium, there is no imposed driving force and so the system is always in the linear-response regime. 2) The GK method can compute the entire heat flux tensor with one simulation. NEMD would require a simulation run for each component of the heat flux vector. There the GK method lends itself much easier to the study of anisotropic effects. 3) A key advantage to the GK method is that it is much less sensitive to finite model size effects because a heat source and sink are not required. Hence the GK method can use much smaller models than the NEMD methods. For example, good results for diamond were obtained with only a 4000 atom model with a dimension of about 2.8 nm. The NEMD method would require a model comparable tot he mean free path length (174 nm).
Of course there are disadvantages of the GK method compared to the NEMD method but I have only discussed the positive attributes of the GK method.
A way to implement the GK in lammps would be beneficial to many researchers. I would be interested in obtaining a copy of any GK source code additions to lammps if anyone has been successful in implementing it.
Bill Evans