How macroscopic, deterministic order emerges from microscopic systems governed by quantum and thermal fluctuations remains a central problem in non-equilibrium statistical mechanics. While classical reaction theories based on linear energy landscapes describe thermally activated processes, they do not fully account for the extreme state localization observed in complex systems such as molecular recognition. Here, we propose the Information-driven Quantum Geometric (IQG) model, a theoretical framework in which measurement-induced feedback modifies the effective free-energy landscape. By combining coarse-grained quantum dynamics with large deviation theory, we show that nonlinear information feedback induces a sharp geometric crossover—termed the Fidelity Cliff—marking a transition from fluctuation-dominated dynamics to deterministic state locking. Numerical analysis based on a nonlinear Fokker-Planck equation demonstrates the formation of a noise-suppressed metastable subspace (NSMS), where an emergent energy gap provides spectral protection against environmental noise. This mechanism ensures robust state localization despite continuous thermal perturbations. Our results establish a unified physical framework linking quantum measurement dynamics to classical reaction kinetics, providing a quantitatively testable mechanism for the emergence of macroscopic attractors in dissipative systems.
How macroscopic, deterministic order emerges from microscopic systems governed by quantum and thermal fluctuations remains a central problem in non-equilibrium statistical mechanics. While classical reaction theories based on linear energy landscapes describe thermally activated processes, they do not fully account for the extreme state localization observed in complex systems such as molecular recognition. Here, we propose the Information-driven Quantum Geometric (IQG) model, a theoretical framework in which measurement-induced feedback modifies the effective free-energy landscape. By combining coarse-grained quantum dynamics with large deviation theory, we show that nonlinear information feedback induces a sharp geometric crossover—termed the Fidelity Cliff—marking a transition from fluctuation-dominated dynamics to deterministic state locking. Numerical analysis based on a nonlinear Fokker-Planck equation demonstrates the formation of a noise-suppressed metastable subspace (NSMS), where an emergent energy gap provides spectral protection against environmental noise. This mechanism ensures robust state localization despite continuous thermal perturbations. Our results establish a unified physical framework linking quantum measurement dynamics to classical reaction kinetics, providing a quantitatively testable mechanism for the emergence of macroscopic attractors in dissipative systems.
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs. When the resolved phase-space area is large compared with Planck's constant, the accessible statistics of any quantum state admit an effective classical description: coarse-grained observables become approximately jointly measurable and the induced probability density is positive. We derive the exact evolution equation for this density and show that, in the strong coarse-graining regime, its non-Liouville corrections are suppressed up to an Ehrenfest time, resulting in classical Hamiltonian flow generated by a Hamiltonian smoothed over the measurement cell. When the Hamiltonian varies negligibly across such a cell, the smoothed Hamiltonian reduces to the classical Hamiltonian whose quantization produced the quantum dynamics, thereby closing the quantization--classical-limit loop. Repeated finite-resolution measurements then generate stochastic records confined, with high probability, to tubes around classical trajectories. Our results provide a unified operational framework for the quantum-to-classical transition in microscopic and macroscopic systems, and establish the consistency of the quantization--classical-limit cycle.
We introduce the Quantum Consensus Principle (QCP), a first-principles framework that provides a purely dynamical derivation of the quantum measurement process without modifying the Schrödinger equation. By treating the apparatus–environment complex as an open quantum system, we show that measurement outcomes emerge from a thermodynamic selection process governed by large-deviation dynamics. Central to the theory is the derivation of a universal selection potential, Φᵢ, which is uniquely determined by the BKM information geometry of the thermal environment and linked to microscopic Hamiltonian parameters via Green–Kubo relations. We rigorously demonstrate that the conditioned system state follows a Hellinger-contractive supermartingale, converging almost surely to unique pointer states. Unlike standard postulates, QCP derives the Born rule as a specific neutrality limit and predicts measurable, apparatus-dependent deviations for non-ideal observers. Furthermore, the theory establishes a characteristic non-monotonic scaling of collapse timescales, providing a clear path for experimental falsification. This work bridges the gap between quantum information theory and non-equilibrium thermodynamics, identifying measurement as a fundamental consensus phenomenon in macroscopic systems.
Abstract We introduce the Quantum Consensus Principle (QCP), a first principles framework that provides a purely dynamical derivation of the quantum measurement process without modifying the Schrödinger equation. By treating the apparatus environment complex as an open quantum system, we show that measurement outcomes emerge from a thermodynamic selection process governed by large-deviation dynamics. Central to the theory is the derivation of a universal selection potential, Ф, which is uniquely determined by the BKM information geometry of the thermal environment and linked to microscopic Hamiltonian parameters via Green-Kubo relations. We rigorously demonstrate that the conditioned system state follows a Hellinger-contractive supermartingale, converging almost surely to unique pointer states. Unlike standard postulates, QCP derives the Born rule as a specific neutrality limit and predicts measurable, apparatus-dependent deviations for non-ideal observers. Furthermore, the theory establishes a characteristic non-monotonic scaling of collapse timescales, providing a clear path for experimental falsification. This work bridges the gap between quantum information theory and non-equilibrium thermodynamics, identifying measurement as a fundamental consensus phenomenon in macroscopi systems.
We develop a geometric formulation of stochastic dynamics in which noise, diffusion, path probabilities, fluctuation theorems, and entropy production arise from the intrinsic geometry of an evolving manifold rather than from externally imposed randomness. Within the theory of moving manifolds, we establish a curvature-noise correspondence: fluctuations are governed by the inverse curvature tensor, while entropy production is controlled by curvature deformation. The invariant continuity law on a moving hypersurface yields a geometric Fokker-Planck equation, and curvature-velocity coupling generates a quadratic Onsager-Machlup functional determining path weights. The resulting entropy functional satisfies a curvature-driven monotonicity law, providing a geometric derivation of the Second Law. In two dimensions, the curvature invariant reduces to Gaussian curvature and encodes topology, so topological transitions produce discrete entropy jumps. When the ambient space carries a Minkowskian signature, the same curvature-kinetic quadratic form that generates dissipative thermal weights produces oscillatory phase weights, and the Laplace-Beltrami operator governing entropy evolution acquires a Schrödinger-type structure. This provides a geometric resolution of the apparent distinction between classical stochastic behaviour and quantum dynamics. These results show that stochastic behaviour, thermodynamic irreversibility, and quantum transition amplitudes are unified within the moving manifold framework. Geometry does not merely accommodate stochasticity; stochastic behaviour arises as a consequence of deterministic geometric evolution. The theory predicts curvature-controlled anisotropic diffusion, entropy jumps at topology-changing events, and a geometric thermal-quantum crossover in which classical stochastic weights and quantum amplitudes are generated by the same curvature-kinetic action.
Measurement in quantum mechanics is commonly treated as a passive observational process that reveals properties of an underlying physical system. However, both theoretical analysis and experimental practice suggest that measurement interactions are physical events that irreversibly alter system states and their subsequent evolution. This work advances the hypothesis that measurement events function as generative interactions that actively produce realized states, rather than merely disclosing pre-existing conditions.Focusing on non-equilibrium dynamics, we examine the role of discrete interaction events in the transition from potential configurations to actualized states. Measurement interactions are characterized as localized, irreversible processes that introduce stable correlations and constrain future system evolution. From this perspective, state realization is associated with event-based commitments rather than continuous revelation, aligning naturally with thermodynamic irreversibility and entropy production.Preliminary conceptual analysis indicates that this generative role of measurement events is consistent with established formulations of quantum theory, including unitary evolution prior to measurement and the statistical structure of observed outcomes. The proposed viewpoint does not modify existing formalism or introduce new dynamical laws, but instead reframes the ontological role of measurement within standard theory.1Analogous event-driven state transitions appear across a range ofnon-equilibrium systems, including thermodynamic processes, information processing, chemical reactions, and distributed computational protocols. These analogies are noted to highlight structural commonalities in state actualization, rather than to assert cross-domain phys-ical equivalence.The present work introduces this hypothesis as a foundational perspective on the role of discrete interaction events in state formation. Broader structural implications and potential extensions of this framework are reserved for future investigation. Keywords: measurement theory, non-equilibrium dynamics, quantum observation, state formation, irreversibility
We develop an interacting extension of the Double Covariance Model (DCM), a stochastic subquantum framework in which macroscopic quantum dynamics emerge through coarse-graining of correlated microscopic fluctuations. Starting from local stochastic differential equations on subsystem Hilbert spaces, we derive a closed evolution equation for a coarse-grained double covariance operator using multi-scale Itô calculus and sliding-window averaging. The construction explicitly incorporates two separated temporal scales: a fast microscopic fluctuation scale governing subquantum stochastic processes and a slower macroscopic observation scale associated with coarse-grained dynamics. Within the hydrodynamic limit, where the ratio between microscopic correlation time and averaging-window scale vanishes, rapidly fluctuating corrections disappear and the effective dynamics converges to a deterministic macroscopic transport equation. We show that the emergent macroscopic dynamics has the exact Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form: coherent Hamiltonian evolution arises from deterministic subquantum flow, while dissipative channels emerge from quadratic noise correlations. The framework further demonstrates how non-separable interaction Hamiltonians can arise from strictly local, state-dependent stochastic feedback fields. In the fluctuation-free limit, the model reduces naturally to the standard von Neumann equation, providing a unified stochastic foundation for both open and closed quantum dynamics.