Density-Driven Free-Energy Gradient Formation as a Scale-Invariant Physical Principle

We identify a common physical structure underlying two independently observed phenomena at vastly different scales: (i) sign-coherent correlations between Cosmic Microwave Background (CMB) temperature residuals and extreme large-scale matter overdensities and underdensities, and (ii) biphasic chemical potential gradients generated by a single metabolically active prokaryotic cell. While the governing equations in each domain differ, both systems exhibit dynamics consistent with free-energy gradient flow driven by localized density contrasts. We formalize this observation using a scale-independent free-energy functional framework and show that the measured observables in both experiments correspond to gradients of an underlying potential. This work does not propose a universal dynamical law, but establishes a shared variational structure: localized density contrasts generically induce free-energy gradients that drive measurable fluxes. The result motivates a unified physical description of organization across scales grounded in non-equilibrium thermodynamics.