Stress tensor virial expression

The term T (Q) is the virial of the forces exerted on the surface of the subsystem, a term expressible in terms of the stress tensor previously defined in eqns (8.173) and (6.12),... 

The final conclusion is that the expression for the stress tensor developed in Sect. 7 is consistent with the tensor virial theorem. Furthermore, it is not permitted to add a divergenceless term to the stress tensor, and the partitioning of the external source term in Eq. (7.9) into an external force term G and the divergence of in Eq. (7.10) is correct. 

For each of the force field contributions described above, there is a corresponding contribution to the total instantaneous stress tensor Lennard-Jones interactions for total energy calculations or for virial calculations of the stresses, long range corrections need to be included, as discussed by In t Veld et al. [26]. 

A different type of structural parameter was considered recently by the present authors, namely X representing a homogeneous macroscopic strain defined as the linear scaling of all particle positions as x- 1+e)x. The e is a constant 3x3 strain tensor, and e=0 corresponds to some reference configuration. The conjugate force is in this case defined as the macroscopic stress a, and an explicit general expression denoted the "stress theorem" is derived by Nielsen and Martin (1983). The result is a generalization of the quantum virial theorem (Born et al., 1926),... 

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