The mathematical operation involved in quantum--classical limits constitutes an active research area. The limit is usually associated with semiclassical expansions or environment-induced decoherence. In this work we argue that a complementary and conceptually sharp characterization is available: the quantum--classical transition can be understood as a flattening of the information geometry underlying quantum state space. From this perspective, \textbf{quantumness is associated with curvature-induced rigidity of probability assignments}, while classical behavior emerges when this geometric rigidity becomes operationally irrelevant. This geometric viewpoint provides a structural criterion for classicality based on the scalar curvature of the information metric and unifies semiclassical limits, decoherence, and thermodynamic coarse-graining within a single framework.
This paper synthesizes the "Anatomical Reviews" to redefine the quantum-classical transition through an intrinsic operator-algebraic framework. It moves away from standard environment-induced decoherence toward a model where classicality emerges from the sectorisation of infinite-dimensional Hilbert spaces within isolated systems. Utilizing the Avalanche Photodiode (APD) model, the study demonstrates that macroscopic definiteness arises from double-exponential divergence in state overlap, creating a rigorous structural transition. The work formalizes this transition as a geometric degeneracy in the quantum Fisher information metric, linking fractal avalanche geometry to Tomita-Takesaki modular theory and providing a falsifiable experimental foundation for the algebraic Heisenberg cut. KSCCN Mamun, SM (2026) ……………………………….1 Algebraic Sectorisation, Information Geometry, and the Quantum-Classical Transition A Synthesis of the Anatomical Reviews (Vol-VI) Also available on Academia.edu: https://www.academia.edu/attachments/133083183/download_file?s=portfolio
This paper presents a geometric–informational model of quantum decoherence formulated in terms of the Forman–Ricci curvature on a weighted graph representing correlations between entangled subsystems. In this framework, decoherence emerges as a curvature–driven process that progressively flattens the informational geometry of the system. The model derives a gradient–flow dynamics from an action principle with dissipation and is quantitatively compared with the experimental results of Bordes et al. (2024) on entangled gamma photons. The proposed formulation establishes a conceptual bridge between the Lindblad formalism and informational geometry, offering a scale–independent interpretation of quantum decoherence as the geometric relaxation of correlation structures, consistently describing both optical and gamma entanglement regimes.