A Mesoscopic Ginzburg--Landau Model for Vibrational Strong Coupling Enhanced Rayleigh Scattering in Molecular Liquids

Recent experiments by Sandeep \textit{et al.} [Angew. Chem. Int. Ed. 65, e16917 (2026)] suggest that vibrational strong coupling (VSC) in molecular liquids can generate mesoscopic phenomena beyond single-molecule observables, including resonantly enhanced Rayleigh scattering, abrupt concentration thresholds, and thermal collapse. Motivated by these observations, we construct a mesoscopic Ginzburg--Landau model with two coupled fields: a cavity-controlled collective vibrational polarization $P$ and a secondary structural field $m$ whose long-wavelength susceptibility is renormalized by the collective vibrational polarization intensity $P^2$, assumed to govern long-wavelength density/dielectric fluctuations. With calibrated parameters, the model captures the observed Rayleigh enhancement, collective scaling relations, and threshold-like behavior, while explaining why polaritonic/IR signatures may persist when Rayleigh scattering disappears. The model further predicts enhanced long-wavelength density/dielectric correlations, enlarged mesoscopic correlation lengths, and slowed structural dynamics in the regime with strong Rayleigh enhancement, providing direct experimental tests through small-angle X-ray/neutron scattering and dynamic light-scattering probes.