Ask HN: Can abstract systems admit stress–potential field equations?
In physics, stress tensors generate curvature or potential fields (e.g. elasticity theory, gravitation, Poisson-type equations).
A very generic form is something like:
∇²φ = −∇·T
where T is a rank-2 stress tensor and φ a scalar potential.
This formalism is usually tied to physical matter, but mathematically it seems much more general.
My question is deliberately narrow:
Is there any mathematical obstruction to applying a stress–potential formulation to non-physical abstract systems? For example: reasoning systems, information flow, symbolic dynamics, or other structured processes. Are there known cases where such formulations provably fail outside physics?
I’m not claiming this should work, only asking whether the restriction to physical systems is necessary, or mostly historical.
Pointers to counterexamples, prior work, or reasons this is ill-posed are very welcome.
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