The Semiclassical Stirling Engine of the Cosmos: Quantum Thermodynamics of the Global Reset, and Open Brane-World Systems in the Stratoverso

We present the definitive thermodynamic and quantum-reset formulation of the Stratoverso Framework (Paper K). Cyclic and multi-layer cosmologies face the outstanding challenge of entropy accumulation — the Tolman paradox — which inevitably leads to cosmological heat death. We resolve this fundamental issue by modeling our four-dimensional FLRW brane-universe as an open quantum system coupled to a five-dimensional warped Anti-de Sitter (AdS5) bulk spacetime. We derive the Lindblad Master Equation governing the density matrix of the brane, showing that the bulk acts as an infinite, cold thermodynamic heat sink that continuously absorbs massive Kaluza-Klein graviton excitations and entropy flux JS. We formalize the four distinct thermodynamic phases of the cosmological layer cycle, showing how the transition at each turning point behaves as a highly efficient semiclassical regenerator. At the terminal ground state (Layer 0), the boundary of the warped space prevents further discrete radion shifts Δχ = ln (1/λ), forcing the universe to impact the absolute holomorphic branch point w=0. We prove that this collision triggers a quantum critical phase transition of BKT type (critical exponent αₜhermo = 0, ν ≈ 0. 5), where the dual boundary CFT partition function undergoes a first-order topological collapse and the 5D bulk curvature diverges as ΔR5 ∝ |χ - χcrit|^-1. Finally, we formulate the global reset as a non-equilibrium quantum tunneling event in the Wheeler-DeWitt superspace. The reset instanton pump-primes the radion field from Layer 0 — the densest, hottest, locally most energetic core — back to Layer 140, the most rarefied and coldest state, regenerating the entire chain from the inside out. The tunneling probability Pᵣeset ≈ e^-476 ≈ 10^-207 indicates a cosmologically ultra-rare but ergodically inevitable event, with a cycle time tcycle ~ tPlanck × 10²07 years, resolving the Tolman paradox without residual entropy accumulation.