Information-Theoretic Limits and Emergent Riemann-Cartan Geometry in Driven Moiré Effective Spacetimes.

This paper establishes a purely theoretical framework and a mathematical toy model exploring the non-equilibrium physics of emergent gravitational topologies and information-theoretic constraints within driven twisted bilayer graphene (tBLG) manifolds. We investigate a highly speculative, exotic quantum gravity scenario where the non-Abelian Berry connection and deformation profiles of a magic-angle moiré lattice serve as a localized analog of a Riemann-Cartan spacetime containing both curvature and torsion fields. By treating a hypothetical low-energy neutrino flux passing through this topological landscape as an open quantum information manifold, we analyze the coherent evolution of mass and flavor eigenstates. Under a high-frequency pulsed driving field, we derive the exact regulared Topological Inversion Operator T(t), coupling the geometric phase shifts to a normalized algorithmic information deficit parameter D_b derived via Umegaki's relative quantum entropy. Using quantum information thermodynamics, we formalize the exact effective transition cross-section (σ_eff) and the corresponding von Neumann entropy reduction rate within the fermion ensemble. Thermodynamic closure and mathematical self-consistency are strictly enforced under the Landauer dissipation limit for open systems. This toy model bypasses the standard weak-force cross-section bottleneck by operating entirely within the geometric boundaries of momentum-space field emulations, offering a scalable mathematical platform for investigating the informational foundations of spacetime and holographic event horizons. ---------------------------------------------------------------------------------------------------------------------- VERSION 2.0.0 — RELEASE NOTES / DESCRIPTION OF CHANGES: This version presents a profound conceptual and structural revision of the manuscript. To preserve strict academic rigor, the paper has been fully repositioned as a rigorous mathematical and information-theoretic toy model within non-equilibrium quantum field theory (NEQFT) and analog gravity: Transition to a Theoretical Toy Model: The abstract, introduction, and conclusions have been completely rewritten to position the research as a speculative toy model exploring quantum gravitational gauge topologies. Removal of the Applied Engineering Framework: The former applied section on physical table-top detection protocols has been entirely removed, resolving critical constraints regarding thermal decoupling and material phase coherence limits at cryogenic temperatures. Microscopic Upgrades: Integrated a self-contained mathematical derivation of the Berry connection using periodic Bloch amplitudes, embedded self-consistent Hartree-Fock mean-field potential parameters, and implemented a non-equilibrium Keldysh diagrammatic analysis to map the impact of structural moiré disorder. Information Thermodynamics: Formalized the operational capacity of the non-local Topological Inversion Operator under strict boundaries, ensuring complete global thermodynamic closure under the Landauer dissipation limit for open systems.