Non-Markovian Quantum Mechanics and Information Thermodynamics in Open Systems: An Analysis of Scale Unification and Coherence Stabilization

This research constitutes the second installment (Paper II) of the T-FINAL Project. Abstract: Following the conceptual framework introduced in Paper I, this work formalizes a physical unification based on Open Systems Dynamics. It is postulated that the quantum vacuum can be modeled as a High-Dimensional Information Bulk (HDIB) —a superior topological stage (D=5) acting as a thermodynamic and computational reservoir from which energy, baryonic matter, and spacetime geometry emerge. The HDIB is mathematically defined through a Generalized Heisenberg spin network on a hypercubic lattice with toroidal topology (T^5) and connectivity z=10. Key contributions of this paper include: • Microscopic Scale: Derivation of a Binary Fractal Resonance from the Shannon-Planck Limit, identifying the N=111 operational window (7.14 GHz) for dephasing mitigation in quantum systems. • Cosmological Scale: An analytical deduction of the critical acceleration a_0 and the transition to the entropic viscosity regime. • Phenomenology: Demonstration that Dark Matter effects are a consequence of scale-invariance breaking caused by the saturation of information flux in the Bulk. This research provides a consistent mathematical framework for understanding scale interactions and offers a thermodynamic alternative to the Dark Matter problem by deriving galactic dynamics from fundamental constants.