The universal law behind long-lived interfaces in fully miscible fluids

Miscible fluids come into contact ubiquitously across biological, industrial, and geophysical systems, yet sharp interfaces are widely assumed to be incompatible with fully miscible mixtures. Contrary to this expectation, sharply defined boundaries are repeatedly observed to form and persist far beyond molecular timescales, while the physical principles governing their emergence and stability have remained elusive. Here, we establish a closed variational theory that resolves this paradox by introducing a co-evolving enthalpic interaction, which couples self-consistently to the interfacial concentration field and evolves through a stepwise minimum-entropy-generation pathway. The theory predicts the emergence of an ultrathin interface governed by an exact Fermi–Dirac concentration profile, followed by deterministic thickening and eventual rupture. It identifies universal, parameter-free quantities, including the minimum nonequilibrium interfacial tension and the lifetime of the interface, in quantitative agreement with experiments on molecular liquids, polymer mixtures, and whole blood. The rupture point is fixed by a universal constant, Λ _c , determined solely by the correlation length of the miscible fluid, rendering interfacial stability and lifetime predictable from first principles. Together, these results unify the birth, endurance, and dissolution of sharp interfaces within a single variational framework, providing a general nonequilibrium phase theory grounded in measurable physical quantities.