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Shannon Entropy as an Order Parameter for the Two-Dimensional Confined Coulomb Systems: Exact Balance Law, Topological Charge Sum Rule, and Boundary Saturation
We establish a complete information-theoretic framework for the known minimum-energy configurations of the two-dimensional Thomson problem on a hard-wall disk, based on the Shannon entropy of the Voronoi topological charge distribution. Two exact results are proven and hold for all studied systems o
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