In our recent work, we introduce the Co-Evolving Variational First Principle (CVFP) to explain the emergence, persistence, and eventual decay of long-lived interfaces in fully miscible fluids.

The key idea is that the interfacial concentration field does not evolve on a fixed thermodynamic landscape. Instead, the Euler–Lagrange solution and the underlying free-energy landscape co-evolve self-consistently as a coupled pair. This hidden variational structure gives rise to optimal nonequilibrium pathways through a sequence of quasi-stationary states.

The framework reveals a dual structure between interfacial enthalpy and concentration-gradient energy, explains why long-lived miscible interfaces can form, and predicts their lifetime quantitatively across different fluid systems. It provides a unified description of the birth, persistence, broadening, and rupture of miscible interfaces within a first-principles variational framework.

The universal law behind long-lived interfaces in fully miscible fluids
Communications Physics 9, 300 (2026)
DOI: 10.1038/s42005-026-02869-0