Force and stress tensor components

Based on Eqs. (6.15)-(6.17b) we can also derive the corresponding expressions for the force acting on particle i, 

Because of Ekjs. (6.16a) and (6.17a) we can split the total force into a sum of three individual contributions, namely 

The reader should realize that the sell-part makes no contribution because the summand in Eq. (6.17b) is independent of the coordinates of particle i. Considering the individual contributions to the total force separately, we obtain after straightforward differentiation 

In writing Eqs. (F.52a) and (F.52b) we have taken into account that the operator V appearing in the original force expression (see Eq. (F.50)] can be replaced by its counterpart Vy with respect to the distance vector r,-j = Tj - Tj where, of course. 

By analogy with Appendix E.3 we derive molecular expressions for various (diagonal) components of the stress tensor (7 — x, y, or z) by realizing that w e may write 

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