The Many Faces of the Quantum–Classical Transition: A Unified Information-Geometric Perspective on Classicality
Abstract
The quantum–classical transition is one of the most frequently invoked concepts in modern physics. Yet the notion of classicality itself is far from unique. Depending on the physical context, classical behavior may be associated with decoherence, the semiclassical limit, thermodynamic averaging, suppression of correlations, emergence of collective order, or geometric simplification of statistical state space. These viewpoints are often presented as if they described a single phenomenon, although they emphasize different physical mechanisms and different operational criteria. In this article we examine the principal notions of classicality that appear across quantum theory, statistical physics, condensed matter physics, and information geometry. We compare the corresponding mechanisms of classical emergence and analyze the physical quantities commonly used to characterize them, including coherence, entanglement, fluctuations, correlation length, Fisher information, statistical complexity, and information-geometric curvature. We argue that many apparently distinct routes toward classical behavior share a common structural feature: a reduction of effective fluctuation freedom. From this perspective, classicality may be interpreted as an emergent regime in which the accessible fluctuation manifold becomes progressively constrained, stabilized, or geometrically simplified. This viewpoint naturally unifies decoherence, semiclassical localization, thermodynamic averaging,…
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