Non-Commutative Rough Battery Dynamics (NC-RBD) Subsuming High-Energy-Density and All-Solid-State Battery Limits via UROA, STCT, and RQIG

All-solid-state and high-energy-density batteries are conventionally bounded by solid-solid interfacial resistance, anode volume expansion, and severe scale-up degradation. This paper supersedes these views by establishing Non-Commutative Rough Battery Dynamics (NC-RBD) within the SMA-∞ Topos. By integrating Universal Rough Operator Algebra (UROA), the Seonggil Theory of Composite Torsion (STCT), and Rough Quantum Information Geometry (RQIG), we prove that interfacial bottlenecks and mechanical stress are topological manifestations of non-commutative boundary friction. Furthermore, interface engineering and scale-up control are formally derived as geodesic entropy minimization subloops and functorial mapping corrections.