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Quantum Reports

The Many Faces of Classicality: An Information- Geometric Perspective

Angelo Plastino

Published Aug 5, 2026• 0 citations
Publisher

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, decorrelation, and collective organization within a common conceptual framework. Rather than representing a unique physical process, the quantum–classical transition appears as a family of related mechanisms through which complex quantum fluctuation structure gives rise to effective macroscopic classical behavior.

DOI
10.3390/quantum8030075

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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, decorrelation, and collective organization within a common conceptual framework. Rather than representing a unique physical process, the quantum–classical transition appears as a family of related mechanisms through which complex quantum fluctuation structure gives rise to effective macroscopic classical behavior.
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.
Quantum entanglement is traditionally described as a statistical correlation encoded in a many-body wavefunction. While this framework successfully predicts measurement outcomes, it leaves unresolved whether entanglement reflects purely probabilistic structure or an intrinsic physical organization of quantum states. Recent experiments have demonstrated that high-dimensional entangled states possess thousands of distinct, experimentally accessible topological invariants that persist under basis changes, noise, and local perturbations. These features are difficult to reconcile with a purely statistical interpretation of the wavefunction, but arise naturally if entanglement corresponds to intrinsic geometric structure within state space. This work analyzes experimental results reported in Nature Communications (2025) showing robust, high-dimensional topological structure embedded in conventional entangled states. We show that the multiplicity, stability, and basis-independence of these invariants support an interpretation of entanglement as intrinsic geometry rather than as observer-dependent probability. Under this interpretation, nonlocal correlations reflect shared geometric structure rather than information transfer, and robustness arises from topological protection rather than statistical averaging. The paper does not modify the formal machinery of quantum mechanics, but reframes the physical meaning of the quantum state. Entanglement is interpreted as a geometric configuration of collective modes whose topology constrains allowed correlations. This perspective provides a natural physical explanation for robustness, nonlocality, and measurement independence, and places strong constraints on interpretations in which the wavefunction is purely epistemic. Together with independent results in condensed matter and gravitational physics, these findings support a geometry-first interpretation of quantum phenomena and contribute to a growing body of experimental evidence that quantum states possess intrinsic physical structure beyond probabilistic description.
We develop an effective gravitational framework for the quantum–classical transition based on the dynamical stability of historical information. Building on previous analyses of gravitational temporal decoherence and the emergence of classical time, the present work addresses the subsequent problem of how classical histories become stable, persistent, and objectively accessible. The framework is formulated as a non-relativistic, semiclassical open-system dynamics in which gravity induces structurally constrained dissipative effects of Lindblad type. Within this setting, we introduce a stability functional that operationally characterizes which quantum states can support robust historical records and which are dynamically suppressed. The quantum–classical transition is described as a smooth, scale-dependent crossover controlled by physically meaningful parameters, rather than as a sharp boundary or interpretational postulate. The emergence of a unique classical past is shown to arise from dynamical selection: while multiple quantum histories are formally allowed, only those supported by stable physical records persist under gravitationally induced dissipation. The framework is explicitly effective in scope and does not rely on a microscopic derivation or full relativistic covariance. Instead, it identifies universal structural features that any viable fundamental theory must reproduce in the appropriate semiclassical regime. This work complements earlier studies on the emergence of classical time by providing a dynamical account of historical stability, thereby contributing to a coherent program for understanding the physical origin of classical reality.
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We develop an information-geometric framework for describing quantum state-update processes associated with measurement and statistical distinguishability. The approach is based on the quantum relative entropy and the quantum Fisher information metric, which together induce a natural Riemannian geometry on the manifold of quantum states. Using the second-order expansion of relative entropy, we show how the Fisher metric governs the local structure of distinguishability between nearby states and defines a corresponding thermodynamic length. This geometric structure provides an effective description of finite quantum state transitions in terms of fluctuation geometry and information-space distance. The formalism is applied to thermal two-level systems and harmonic oscillator states, illustrating how the Fisher metric encodes susceptibilities, fluctuations, and geometric transition costs. We also discuss the relation between thermodynamic length, dissipation bounds, and optimal paths in state space. Within this framework, wave function collapse is interpreted not as a microscopic dynamical mechanism, but as an effective state-update process that admits a geometric characterization in the manifold of density operators. The resulting perspective unifies concepts from quantum information theory, thermodynamics, and differential geometry within a common operational framework based on statistical distinguishability. Possible connections with quantum speed limits, entanglement geometry, and holographic relations between relative entropy and gravitational dynamics are briefly discussed.
Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We focus on microcanonical and canonical ensembles, looking at the geometric counterpart of Gibbs ensembles for distributions on the space of quantum states. We show that one can define quantum heat and work in an intrinsic way, including single-trajectory work. We reformulate thermodynamic entropy in a way that accords with classical, quantum, and information-theoretic entropies. We give both the first and second laws of thermodynamics and Jarzynki's fluctuation theorem. Overall, this results in a more transparent physics than conventionally available. The mathematical structure and physical intuitions underlying classical and quantum dynamics are seen to be closely aligned. The experimental relevance is brought out via a stochastic model for chiral molecules (in the two-state approximation) and Josephson junctions. Numerically, we demonstrate this invariably leads to the emergence of the geometric canonical ensemble.