Structural axioms plus PDE-level reduction consistency when merging identical phases uniquely fix the free-energy density to ideal mixing plus symmetric mean-field interactions and quadratic gradients, and the Onsager mobility to pairwise-exchange form with bilinear degeneracy.
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Mixture-aware closure of the N-phase Navier--Stokes--Cahn--Hilliard mixture model
Structural axioms plus PDE-level reduction consistency when merging identical phases uniquely fix the free-energy density to ideal mixing plus symmetric mean-field interactions and quadratic gradients, and the Onsager mobility to pairwise-exchange form with bilinear degeneracy.