Entropy as Geometric Conflict in Nonequilibrium Steady States: A Fractal Optimum near D ≈ 1.89

We present a geometric framework that interprets entropy production in open nonequilibrium systems as an integral measure of the conflict angle between the energy gradient ∇E and the topologically allowed subspace M. Within a reduced nonequilibrium steady-state (NESS) model, this leads to an effective functional ΔS (D, α) that exhibits a unique interior maximum at D* ≈ 1. 89. Experimental analysis of 74 SEM and TEM images of multi-component nanomaterials synthesized by the hydrodynamic cavitation method yields a mean Hausdorff dimension Dbox = 1. 908 ± 0. 059. Notably, TEM images of hydrofullerenes C₆₀ (OH) ₙ systematically cluster closer to the model optimum (≈ 1. 85), while SEM images give slightly higher values (≈ 1. 94). The results confirm the existence of an effective fractal attractor near D ≈ 1. 89 in cavitation-driven self-assembly. This optimal regime provides the most efficient combination of coherence and dissipation, opening the prospect of creating metamaterials with fundamentally new functional properties that substantially exceed the capabilities of traditional materials. - Version 3 Update Notes: The core manuscript text, theoretical framework, and experimental data remain completely unchanged from the previous version. This update reflects an addition to the author list (inclusion of co-author Volodymyr Hamalii) and minor formatting adjustments to the title page, including the consolidation of affiliations and ORCID placements.