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.
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.
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.
At present there is a consensus about the fact that the emergence of the classical world from the underlying quantum reality involves the physical phenomenon of decoherence, which is usually studied in the version proposed by Zurek and his collaborators. According to this version, decoherence is a process resulting from the interaction between a quantum system and its environment (environment-induced decoherence, EID); this process singles out the observables that receive definite classical values. The aim of this paper is to propose a top-down approach to decoherence, which takes the perspective of the whole closed system, and considers whether each set of degrees of freedom decoheres or not. This approach is more general than the orthodox open-system perspective and dissolves some of its conceptual problems. Although decoherence becomes relative to the way in which the closed system is decomposed, the quantum-to-classical transition defines unequivocally the realm of classicality by identifying the observables with classical-like behavior.
We develop a covariant open-system framework in which spacetime curvature directly governs the decoherence of quantum fields on curved backgrounds. Starting from a geometric deformation of the matter wavefunctional and using standard microlocal assumptions, we derive a curvature-dependent Lindblad equation whose local decoherence rate is fixed by scalar curvature invariants through the influence of metric fluctuations. Within this setting we establish a general purity-decay theorem: the reduced state seen by any semiclassical observer undergoes monotonic purity loss, and complete mixing occurs precisely when the curvature-dependent effective rate diverges. To characterize the associated information flow, we construct a geometric entropy func- tional inspired by Perelman’s H-entropy and show that it obeys a monotonicity relation under the induced information-theoretic flow. Finally, we explain how the semiclassical appearance of information loss produced by curvature-driven decoherence is reconciled with global unitarity once nonperturbative gravitational saddles—replica wormholes and quantum extremal surfaces—are included. The resulting picture integrates curvature-induced deco- herence, geometric entropy production, and the unitary Page curve into a single coherent framework.
Quantum geometry is conventionally understood as a descriptive structure characterizing the space of quantum states. In this work, we examine an alternative but fully compatible interpretation in which geometric quantities—such as Berry curvature and the quantum metric—function effectively as constraint layers shaping the set of admissible dynamical trajectories. Without introducing new degrees of freedom or modifying established theoretical frameworks, we analyze how geometric terms enter semiclassical equations of motion and transport responses in quantum systems. In particular, anomalous velocity contributions and geometry-dependent transport coefficients indicate that geometry operates not merely as a passive descriptor, but as an active structural condition on system evolution. This shift from geometry as description to geometry as constraint does not alter the formalism, but reorganizes its interpretation, reducing conceptual fragmentation by unifying diverse geometry-dependent effects under a common structural principle. It highlights that the evolution of quantum systems is not only governed by dynamical variables, but also by the geometric structure that restricts the space of accessible trajectories. This perspective suggests that transport phenomena may be more fruitfully analyzed through constraint-space formulations rather than purely state-space descriptions. We clarify the scope and limits of this reinterpretation, emphasizing that it introduces no new physical interactions or ontological commitments. Instead, it provides a conceptually sharper and operationally informative framework for understanding the role of geometry in quantum dynamics and transport.
The unification of quantum mechanics and geometric frameworks has historically relied on the formulation of state spaces as Riemannian or Kähler manifolds, wherein geometric properties such as the Fubini-Study metric and Berry curvature govern quantum evolution and fidelity. However, the physical consequences of these geometric structures have traditionally remained confined to abstract informational and phase-related phenomena, rarely translating into direct mechanical or dynamical forces within physical systems. This paper introduces the comprehensive theoretical framework of Quantum-State Curvature Pressure, designated as QSCP, which posits that the intrinsic curvature of quantum state spaces can act as a source of physical pressure. By defining a quantum-state metric tensor denoted as g_ij and introducing a scalar curvature of the quantum state space denoted as R_Q, we establish a thermodynamic and mechanical analogy where variations in state volume, denoted as V_state, induce a scalar pressure field. Specifically, the quantum-state curvature pressure is formulated as P_Q = -kappa * (partial R_Q / partial V_state). Consequently, alterations in quantum state paths and manifold deformations give rise to an emergent effective force defined as F_Q = -grad P_Q. This framework successfully bridges the chasm between abstract quantum geometry and tangible mechanical dynamics, offering profound implications for quantum control, quantum thermodynamics, and the fundamental interpretation of quantum-induced forces without relying on conventional environmental decoherence or external classical potentials.
This paper proposes a fundamental framework based on information geometry that unifies quantum mechanics, thermodynamics, and spacetime geometry into a single foundational theory. Starting from three elementary axioms regarding information as the primary physical ontology, we derive the universal information metric, construct the information action functional, and show that all known physical laws emerge as extremal conditions of this functional. The theory recovers standard quantum mechanics, classical thermodynamics, and general relativity in appropriate limits, while predicting new relations between quantum entanglement, gravitational curvature, and entropy. We conclude that all physical phenomena—matter, energy, spacetime, and interactions—are equivalent to geometric structures on the space of quantum information states.