The single-threshold model of the quantum-to-classical transition treats classicality as a binary crossing of a single Imass criterion. This paper argues that the transition is better described by a dual-parameter structure: a lower threshold α at which coherence becomes operationally negligible, and an upper threshold β at which classical distinguishability becomes stable against perturbation. The interval [α,β] constitutes a hysteresis gate within which the transition is directionally asymmetric — re-coherence remains possible below β but is operationally suppressed beyond it. A spectral decomposition of informational mass (Imass) is introduced, resolving the total accumulated environmental distinguishability into mode-resolved contributions. This decomposition enables precise characterisation of entropy plateau conditions: regions of near-zero entropy growth arising when dominant spectral modes have saturated while subdominant modes continue accumulating slowly. As a derived consequence of the dual-threshold structure, the framework predicts Mpemba-like trajectory crossings between systems initialised at different Imass values. A system with higher initial Imass can exhibit lower entropy than a system with lower initial Imass at intermediate times, owing to earlier entry into the entropy plateau regime. This prediction is mechanistically distinct from existing quantum Mpemba results and constitutes a testable consequence of the framework. A minimal three-level qutrit Lindblad model is developed to illustrate the dynamics numerically.
The single-threshold model of the quantum-to-classical transition treats classicality as a binary crossing of a single Imass criterion. This paper argues that the transition is better described by a dual-parameter structure: a lower threshold α at which coherence becomes operationally negligible, and an upper threshold β at which classical distinguishability becomes stable against perturbation. The interval [α,β] constitutes a hysteresis gate within which the transition is directionally asymmetric — re-coherence remains possible below β but is operationally suppressed beyond it. A spectral decomposition of informational mass (Imass) is introduced, resolving the total accumulated environmental distinguishability into mode-resolved contributions. This decomposition enables precise characterisation of entropy plateau conditions: regions of near-zero entropy growth arising when dominant spectral modes have saturated while subdominant modes continue accumulating slowly. As a derived consequence of the dual-threshold structure, the framework predicts Mpemba-like trajectory crossings between systems initialised at different Imass values. A system with higher initial Imass can exhibit lower entropy than a system with lower initial Imass at intermediate times, owing to earlier entry into the entropy plateau regime. This prediction is mechanistically distinct from existing quantum Mpemba results and constitutes a testable consequence of the framework. A minimal three-level qutrit Lindblad model is developed to illustrate the dynamics numerically.
The quantum-to-classical transition is commonly described through decoherenceand environmental entanglement, yet quantitative measures of structured phaseorganisation within coherent quantum states remain comparatively underdeveloped.This work introduces a phase-organisation functional that measures the structuredphase separation encoded in the off-diagonal coherence channels of a quantumdensity matrix. The functional characterises the progressive conversion ofcoherent phase structure into environmentally encoded branch distinguishabilityduring open-system evolution. A minimal two-state model illustrates the evolution of phase organisation underdecoherence. Environmental degrees of freedom are modelled as distributedphase-encoding channels whose cumulative phase dispersion suppresses coherenceexponentially. An effective informational persistence quantity, termedinformational mass (Imass), is introduced operationally as a measure ofaccumulated environmental branch distinguishability. The framework connects phase accumulation, decoherence, entropy growth, andclassical distinguishability within a unified informational description whileremaining fully compatible with standard open quantum systems theory. Potentialapplications to coherence monitoring and hybrid quantum-classical architecturesare discussed. This is a working paper deposited to establish a citable DOI record.The framework is exploratory; limitations and open questions arediscussed explicitly in the paper. Part of the Q2C Research Initiative theoretical series. This paper establishes the phase-organisation functional and single-threshold Imass criterion as the foundational framework for the programme. Paper 2 (dual-parameter threshold structure, spectral Imass, entropy plateau conditions, and Mpemba-like trajectory crossings) is available at https://doi.org/10.5281/zenodo.20531722. Paper 3 (σ-algebra filtration structure) is in preparation.
The quantum Mpemba effect describes the unusual relaxation of a quantum system where if starting from a state far from equilibrium reaches equilibrium faster than starting from a closer state. In this work, the steepest-entropy ascent quantum thermodynamics framework is used to model this effect in a three-level ion system coupled to a short-life level which acts as an environment. The four-level Hilbert space is reduced to an effective three-dimensional description via the Feshbach projection, where the resulting model parameters are determined by a differential evolution algorithm. Predictions of both the steepest-entropy-ascent and Lindblad frameworks agree well with experimental data for all three initial conditions considered. In addition it is shown that, independently of the Mpemba condition, the relaxation parameter τD is an emergent thermodynamic quantity whose step-function time dependence arises from a near-indetermination at the metastable state, resolved by the two-timescale structure of the dissipative dynamics, with a step height τD+/τD−(∣λf∣/∣λs∣)r set by the ratio of the linearised relaxation rates at the metastable state times a geometric factor r fixed by the curvature of the entropy and free-energy-variance surfaces there. Furthermore, it is also established the correspondence between the Lindblad and steepest-entropy-ascent order parameters as spectral and geometric suppression of the same slow dissipative mode, and it is shown that for isolated systems with a negative nonequilibrium inverse temperature, as realized in the case studied here, the genuine Mpemba free-energy ordering is equivalent to an entropy ordering.
The quantum measurement problem—why observation appears to collapse superposition states—has resisted resolution despite decades of progress in decoherence theory. While environmental decoherence explains the emergence of classicality, it lacks a quantitative criterion distinguishing "measured" from "merely decohered" systems. This work proposes such a criterion: measurement occurs when environmental coupling strength, quantified by the dimensionless parameter W = (I * tau) / tau0, exceeds a universal threshold W0. Here I is path distinguishability (Englert’s D), tau is information retention time, and tau0 is system coherence time. The framework predicts continuous visibility decay V(W) = 1 / [1 + exp(kappa * (W - W0))] rather than binary collapse, with threshold W0 ≈ 1–3 across platforms after normalization. Testable predictions include: (1) I × tau trade-off (different combinations of distinguishability and retention yielding identical visibility at matched W); (2) quantum eraser timing dependence (recovery window ~ tau0); and (3) finite collapse propagation speed, formalized as the Causal Limit Postulate (v = c in vacuum). The model predicts a measurable delay (Delta t ≈ L / c) and introduces Causal Viscosity, where n_eff ~ Gamma^(1/2), to describe propagation drag in decohering media. A cavity-QED toy model with 87Rb atoms validates the framework with realistic parameters, independently confirmed by dispersive regression.
Redundancy-Limited Emergence of Classical Histories in Quantum Systems This work investigates how classical reality emerges from underlying quantum dynamics, focusing on the role of environmental information, noise, and fundamental entropy limits. In quantum theory, systems evolve into superpositions of many possible outcomes. However, in practice we observe a world with definite, classical histories. A widely accepted explanation is decoherence, in which interactions with the environment suppress interference between different quantum states. More recent developments, particularly in quantum Darwinism, emphasize that classical information becomes objective when it is redundantly recorded across many independent parts of the environment. This paper addresses a key unresolved question: how many distinct classical histories can physically exist? To answer this, we construct a minimal computational model in which a system’s history is encoded into multiple environmental fragments, each subject to noise. By computing how much information about the system can be recovered from subsets of these fragments, we identify a characteristic scale that determines how many fragments are required to reconstruct the system’s history. Our results reveal a simple and robust relationship: the ability to recover classical information depends on the entropy of the noise affecting environmental records. As noise increases, more fragments are required to reconstruct a history, reflecting a loss of distinguishability. This leads to the definition of a “recoverability factor,” which quantifies how efficiently entropy can be converted into usable, classical information. We then connect this information-theoretic result to fundamental bounds from gravitational physics. In particular, existing entropy bounds limit the total amount of information that can pass through a region of spacetime. We show that only a fraction of this entropy—determined by the recoverability factor—can contribute to distinguishable classical histories. This leads to a new principle: the number of classical histories is not limited only by total entropy, but by the efficiency with which that entropy can be encoded, preserved, and accessed. Applying this framework to cosmological entropy estimates, we derive explicit upper bounds on the number of distinguishable classical histories in the observable universe. While this number is extraordinarily large, it is nonetheless finite and strongly constrained by both entropy and noise. These results refine the standard picture of quantum branching. While quantum theory allows a vast number of possible outcomes, only a subset can become physically meaningful in the sense of being stable, redundantly recorded, and accessible to observers. More broadly, this work provides a quantitative bridge between decoherence theory, information theory, and gravitational entropy bounds. It suggests that classical reality is fundamentally constrained not just by physical laws governing entropy, but by the efficiency of information transfer within those constraints.
This paper develops the regime‑based structure of the coherence parameter c(t) as the organising principle of Level‑1 representational physics. Building on the stabilisation criteria and state‑mapping formalism introduced in Paper 12, it identifies three coherence regimes—high‑c, intermediate‑c, and low‑c—and shows how major quantum and relativistic phenomena arise as direct consequences of transitions between these regimes. Decoherence is reformulated as a fundamental representational drift driven by the monotonic decrease of c(t), rather than as an environment‑induced process. Tunneling is reinterpreted as bandwidth exit: a Level‑1 mode becomes evanescent in low‑coherence regions and reappears when stabilisation becomes possible again. Entanglement and Bell violations are described as manifestations of shared Level‑1 modes, whose breakdown under decreasing coherence naturally yields classical correlations. Horizon‑like behaviour emerges as a coherence boundary rather than a geometric surface. The resulting framework unifies decoherence, tunneling, entanglement, Bell inequalities, and horizon phenomena under a single representational principle. Paper 13 thus provides the dynamical bridge between the operational constructions of Paper 12 and the empirical analyses developed in Paper 14.
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.