Dear Bill Evans,
I am not sure if the mean free path argument is valid. Typically the mean free path of phonons in crsytals is a function of frequency, not a fixed value. In fact, regardless if you are in equilibrium or not, you can have very long mean free paths even at high temperatures -e.g. low frequency acoustic phonons. I agree with points 1 and 2, and partially with 3. But for point 3 I think that GK is less sensitive to the molecular size because the scattering rates are controlled by the anharmonicity of the potential and the number of phonon present in the system. Hence, even for small molecular domains the number of phonons in your crystal can be large enough to obtain similar relaxation times to those obtained for a larger (bulk) crystal. Moreover, unlike a quantum system, in a classical system phonons (or vibration modes to be precise) interact with slightly relaxed scattering rules, where the anharmonicity might open extra channels for phonons to interact.
On the other hand, I am not sure if the MP method can be classified as a NEMD, since it conserves energy and moment. I guess that if the perturbation (temperature gradient) is small, it could be also classified as EMD.
Regards, Javier
Many thanks to both Bill and Javier for their very insightful and helpful remarks. I believe the MP method is appropriately classified as non-equilibrium because the algorithm is moving energy through the system (i.e. doing work).
For any LAMMPS users relatively new to the field of thermal conductivity calculations via MD, I highly recommend the following papers for their in depth discussions of the points raised by Bill and Javier (and others):
*** P. K. Schelling, et al.; “Comparison of atomic level simulation methods for computing thermal conductivity”; Phys. Rev. B, v 65, #144306 (2002)
Related to this is the following reference (which also touches on Javier’s comments regarding frequency dependence, by discussing the spectral Green-Kubo formulation):
*** S. G. Volz and G. Chen; “Molecular dynamics simulation of thermal conductivity of silicon crystals”; Phys. Rev. B, v 61, pp. 2651-2656 (2000)
An excellent reference specific to carbon nanotube thermal conductivity calculations via MD is:
*** J. R. Lukes and H. Zhong; “Thermal conductivity of individual single wall carbon nanotubes”; Jnl. of Heat Trans., v 129, pp. 705-716 (2007)
Lastly, F. Muller-Plathe’s original paper presenting the MP method points out that the focus therein is on an isotropic fluid where thermal conductivity can be taken as a scalar:
*** F. Muller-Plathe; “A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity”; J. Chem. Phys., v 106, pp. 6082-6085 (1997)
There are other references for interested researchers but those above represent a good start to understanding ins and outs of such calculations.
Have fun!
Ed