How does the stress-energy tensor account for potential energy in static systems?

Question

I see that the definition of the stress-energy tensor refers to the flux of momentum across a surface but given the example of a collection of electrons confined to a box (volume in space), even with no macroscopic flow, the potential energy of the electrostatic repulsion between the electrons would surely contribute to the stress-energy of the system? A similar scenario with neutral particles would have less energy correct? But if the stress-energy tensor is defined in terms of flux, and there is no flow of mass in the box, then how is this potential energy accounted for?

All of the examples I have seen dealing with the stress-energy tensor discuss ideal fluids. I assume this model can actually be applied to any arbitrary configuration of matter, accounting for non-ideal characteristics such as molecular bonding and electrostatic potential energy?

Answer 1

The stress in an arbitrary condensed phase can be expressed atomistically as given here. As you can see, there are two contributions to the stress: a kinetic energy term and a work term. At low temperatures, or even at room temperature in crystals, the work term dominates the stress. In liquids though, the kinetic term dominates.