Virial stress is a measure of mechanical stress on an atomic scale. It is given by
- and are atoms in the domain,
- is the volume of the domain,
- is the mass of atom k,
- is the ith component of the velocity of atom k,
- is the jth component of the average velocity of atoms in the volume,
- is the ith component of the position of atom k, and
- is the ith component of the force applied on atom by atom .
At zero kelvin, all velocities are zero so we have
This can be thought of as follows. The τ11 component of stress is the force in the x1-direction divided by the area of a plane perpendicular to that direction. Consider two adjacent volumes separated by such a plane. The 11-component of stress on that interface is the sum of all pairwise forces between atoms on the two sides.
In an isotropic system, at equilibrium the atomic pressure is usually defined as
It's worth noting that some articles and textbook  use a slightly different version of the equation
where is the ith component of the vector oriented from the th atoms to the kth calculated via the difference
Both equation being strictly equivalent, the definition of the vector can still lead to confusion.
- Allen, MP; Tildesley, DJ (1991). Clarendon Press, ed. Computer Simulations of Liquids. Oxford. pp. 46–50.
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