heat flux in terms of stress

Dear LAMMPS community - I'm trying to track down a derivation
(ideally a published reference) for the expression that LAMMPS uses for
the heat flux in terms of the per-atom virial stress, in particular as it
applies to many-body potentials. I found two relevant threads in the mailing
list archives:

The first cites a paper in J Chem Phys, but while I see the expressions for
the heat flux for a 3-body potential, I don't see any relation to the stress, at
least not explicitly. The second doesn't seem to have a followup from Reese
in the archive.

Is it somehow in that paper and I'm missing it, or is there another
reference I might be able to look at that derives the expression that
LAMMPS uses?


Noam Bernstein
Center for Computational Materials Science
NRL Code 6390
[email protected]

Reese can answer this. So far as I know,
using a many-body potential doesn’t affect
compute heat/flux. If you are asking how

the per-atom virial is calculated for many-body
interactions, then that is discussed (briefly)
on the compute pe/atom doc page. Compute
heat/flux just uses what compute pe/atom
calcluates. This paper
has more details on the many-body virial:

General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions, A. P. Thompson, S. J. Plimpton, W. Mattson, J Chem Phys, 131, 154107 (2009).


Thanks Steve. On second look, I now realize the relation between site virial
and heat flux really is in the J Chem Phys article that was mentioned in
the previous thread, in the Appendix which I hadn't initially read carefully enough.
The reference for the many body stress is helpful as well.