Tunable Hyperuniformity and Hidden Information in Random Cellular Structures

Hyperuniform systems possess the isotropic microstructure of liquids while suppressing large-scale density fluctuations with crystal-like precision, endowing them with exotic optical and transport properties. However, generating these states typically relies on top-down algorithmic optimizations that lack physical realism, leaving the fundamental mechanical and thermodynamic limits of such disordered order largely unexplored. Here, we utilize a mechanical vertex model to explore physical conditions that drive self-organized hyperuniformity in this model. By tuning cortical elasticity and interfacial tension, we engineer a continuous spectrum of effectively hyperuniform states. Crucially, hyperuniformity and rigidity are independently tunable in this system: hyperuniform states occur on both sides of the solid--fluid transition, and the degree of hyperuniformity is set by cell mechanics rather than by the onset of rigidity. Building on these states, we introduce the Hyperuniform Poisson Ensemble (HyPE), constructed by overlaying independent hyperuniform subsets. HyPE states preserve long-range hidden order while asymptotically approaching Poissonian randomness at short length scales, establishing universal scaling relations for density fluctuations. As the most disordered hyperuniform systems reported, HyPEs exhibit vanishing configurational entropy, establishing a fundamental thermodynamic lower bound for the information content of hyperuniform matter. By bridging cellular mechanics with the statistical physics of hidden information, this framework provides a universal blueprint for designing multifunctional metamaterials, with direct applications in photonic bandgap engineering, phononic control, and stress-responsive composites.