Thermodynamics from Frame Exhaustion at Gravitational Horizons

Arc V — Gravity & Quantum Theory Paper 6 Title Accessibility, Thermodynamics, and the Quantum Gap:Why Purification Is the Minimal Structural Upgrade Zenodo DOI 10.5281/zenodo.18225996 Description This paper addresses the structural gap between classical accessibility-based physics and quantum theory. While finite accessibility accounts naturally for horizons, thermodynamic irreversibility, and emergent geometry, it does not by itself explain quantum coherence, entanglement, or unitary evolution. This discrepancy is identified as the quantum gap. The analysis shows that classical accessibility dynamics generically lead to mixed states and irreversible information loss. To recover quantum phenomena, an additional structural principle is required. The paper argues that purification—the requirement that every mixed state arise from a larger pure state—is the minimal and unique upgrade capable of closing this gap without introducing geometric or ontological assumptions. Thermodynamic behavior is reinterpreted as accessibility collapse within a larger purified state space. Entropy emerges from marginalization over inaccessible degrees of freedom rather than from microscopic counting. The paper demonstrates that purification restores reversibility and coherence while remaining fully compatible with operational constraints. By isolating purification as the sole necessary extension beyond finite accessibility, the work sharply constrains possible routes from classical operational physics to quantum theory. Any alternative upgrade is shown to either over-assume structure or fail to recover core quantum features. Keywords purification; quantum foundations; thermodynamics; entropy; accessibility collapse; mixed states; operational quantum theory Notes Arc V — Gravity & Quantum Theory (structural bridge to quantum theory) Identifies the “quantum gap” in accessibility-based physics Purification isolated as the minimal necessary structural upgrade Thermodynamics reinterpreted as marginalization over inaccessible degrees Sets the foundation for post-geometric quantum mechanics