The Relational KMS Interpretation and the Thermodynamic Arrow. Part V: Non-Equilibrium Modular Statistical Mechanics, Open Quantum Systems, and the Topological Resolution of Maxwell's Demon Within a 4D Block Universe

This paper constructs a non-perturbative, structurally consistent thermodynamic formulation of the 4D Block Universe, extending the foundational mathematical frameworks established in Parts I, II, III, and IV of this research series. We provide a rigorous resolution of the thermodynamic arrow of time, quantum decoherence, and Maxwell's demon within a fundamentally timeless, holistic quantum geometry. By shifting the mathematical paradigm from partial trace operations over von Neumann factors of type III_1 to state restrictions on the canonical crossed product algebra (M_III_1 crossed with R), we demonstrate that the Second Law of Thermodynamics is not a fundamental property of the space-time continuum, but an emergent operational constraint dictated by the relational modular automorphism group of Tomita-Takesaki.Quantum decoherence is reformulated as a Generalized Uncertainty Principle (GUP) driven non-linear phase-dampening process, where the environment's mode density (approximately 10^120) scales the Lindbladian coupling constants. Maxwell's demon is topologically exorcised by proving that any information-processing entity is bounded by the non-commutative coordinate jitter, locking Landauer's erasure principle to the minimal area gap of Loop Quantum Gravity (LQG). Finally, we propose strict Popperian falsification criteria and computational methods for verifying these non-equilibrium topological invariants using high-performance quantum simulators (QuTiP) and cosmological polarization data (Planck/BICEP).