Abstract Classical coherence C_cl is introduced as the normalised mutual information C_cl(A,B) ≜ I(A;B)/H(A,B) for finite discrete biological observables. The measure is bounded in [0,1], satisfies five elementary information-theoretic properties, and admits a conditional geometric interpretation as the correlational component of the Fisher–Rao metric under equal-frequency discretisation (local second-order equivalence near the independence manifold). A complete measurement protocol (equi-marginal discretisation, KPSS + Pettitt stationarity checks, change-point handling) is supplied together with sensitivity analysis across copulas, sample sizes, and noise. Thresholds are derived exclusively from system-specific calibration against an independent gold-standard (e.g., carbon flux). This yields the falsifiable Prediction P1 for homeostatic stability in mycorrhizal–host systems. Network superadditivity is left as an open problem. Version 11 deepens the operator-theoretic foundations shared with Fisher information geometry, integrates C_cl into the Architecture of Regulatory Coherence (ARC) and Coherence–Decoherence–Recoherence (CDR) cycle, and explicitly links the framework to the General Theory of Regulated Stability (GTRS) across quantum and cosmological scales. The framework supplies a rigorous classical benchmark for the Quantum Homeostasis Programme.
Abstract Classical coherence C_cl is introduced as the normalised mutual information C_cl(A,B) ≜ I(A;B)/H(A,B) for finite discrete biological observables. The measure is bounded in [0,1], satisfies five elementary information-theoretic properties, and admits a conditional geometric interpretation as the correlational component of the Fisher–Rao metric under equal-frequency discretisation (local second-order equivalence near the independence manifold). A complete measurement protocol (equi-marginal discretisation, KPSS + Pettitt stationarity checks, change-point handling) is supplied together with sensitivity analysis across copulas, sample sizes, and noise. Thresholds are derived exclusively from system-specific calibration against an independent gold-standard (e.g., carbon flux). This yields the falsifiable Prediction P1 for homeostatic stability in mycorrhizal–host systems. Network superadditivity is left as an open problem. Version 11 deepens the operator-theoretic foundations shared with Fisher information geometry, integrates C_cl into the Architecture of Regulatory Coherence (ARC) and Coherence–Decoherence–Recoherence (CDR) cycle, and explicitly links the framework to the General Theory of Regulated Stability (GTRS) across quantum and cosmological scales. The framework supplies a rigorous classical benchmark for the Quantum Homeostasis Programme.
Abstract This paper introduces Quantum Homeostasis as an interpretive framework for understanding quantum decoherence, superposition, and recoherence through the concept of boundary regulation. Rather than treating decoherence as wavefunction collapse triggered by observation, the framework recharacterises it as boundary saturation—the point at which a system can no longer sustain unresolved ambiguity within its regulatory capacity. Superposition is reframed as tolerated ambiguity: a condition in which multiple incompatible configurations coexist within stable boundary conditions. Recoherence is understood not as a return to a prior state but as recovery into a new homeostatic configuration. The framework draws disciplined structural comparisons across quantum, cognitive, and biological systems without asserting metaphysical equivalence between domains. No new physical formalism is proposed. The aim is interpretive clarification: to offer a process-level vocabulary that may help researchers think more precisely about how stability persists through ambiguity across scale. The paper explicitly identifies its own limits and non-claims. Keywords: quantum homeostasis, decoherence, boundary regulation, superposition, recoherence, process isomorphism, interpretive framework
Abstract Across quantum foundations, gravitational physics, and high-energy astrophysics, a recurring structural pattern is observed: systems exhibit delayed responses, threshold-dependent transitions, and stabilising behaviour that resists simple characterisation as entropy maximisation, teleological control, or external optimisation. This paper introduces Ecological Homeostasis (EH) as a structural interpretive framework — not a physical theory — for identifying and describing this class of regulatory behaviour. EH denotes constraint-driven feedback and relational mismatch as the structural basis of stability in physical systems. The framework introduces no new dynamical laws, no new equations, no new observables, and no modifications to General Relativity, Quantum Field Theory, or ΛCDM cosmology. Its value lies in providing a shared conceptual vocabulary that reduces category errors when patterns of regulation are discussed across domain boundaries. The paper defines EH formally, illustrates its interpretive application to non-thermodynamic decoherence and gravitational boundary phenomena, states explicitly what EH is not, and assesses its value as a tool for conceptual clarity. It is designed to stand alone, to be safe to cite, and to remain useful even if no further work on EH is undertaken. Keywords: ecological homeostasis, structural regulation, decoherence, quantum foundations, gravitational systems, conceptual framework, category error, relational mismatch
Two recent results suggest Hamming distance organizes quantum coherence dynamics, but no unified framework connects them. We establish the Hamming Persistence Principle: quantum correlations at Hamming distance persist with amplitude scaling as e−κd, where κ depends on context but the geometric structure is universal. The principle unies two independent discoveries: (1) In open systems under local noise, density matrix elements decay as ρij(t) = ρij(0)e−γH(i,j)ta theorem following from locality of interactions. (2) In isolated systems, Strasberg et al. observed numerically that o-diagonal elements of the decoherence functional correlate negatively with Hamming distance, but noted they had no elaborate theoretical explanation. We provide that explanation: both phenomena arise because physical interactions are local, making Ham-ming distancethe minimum number of single-bit operations connecting two congurationsthe dynamically privileged metric. Numerical verication conrms the framework: (i) Coherence magnitude decreases with Hamming distance(r =−0.26, p < 10−70), reproducing Strasberg's Figure 12. (ii) The decay coecient scales as α ≈0.5 ln D(r= 0.965), supporting the locality derivation. (iii) Maverick histories that deviate from Born statistics cluster at smaller Hamming distance (3/4 tests p < 0.05) and are 2×more coherent with each otherexplaining why they recohere together. The synthesis resolves why entanglement fails to predict decoherence rates: entanglement ignores Hamming geometry. It also suggests a geometric origin for branch selection: histories spread across Hamming space (large D∗H) are stable, while clustered histories (small D∗H) recohere away. The classical world may emerge not from environmental monitoring but from the intrinsic geometry of conguration space.
This research introduces a novel quantitative framework for understanding one of the most fundamental questions in theoretical physics: How and when do quantum systems become classical? By developing a normalized Quantum Persistence Function (QPF) , we provide a continuous measure of residual quantum coherence in open systems interacting with their environment. The framework is rigorously derived from the spin-boson model—a paradigm for studying decoherence—and distinguishes between Markovian (memoryless) and non-Markovian environments based on spectral density structure (Keywords) Quantum decoherence Inflationary cosmology Open quantum systems Quantum–classical transition Primordial perturbations Cosmic Microwave Background Non-Gaussianity Spin-boson model Environmental entanglement Planck mission
We present the Effective Field Theory of Information Reconstruction (EFIR), a mathematically rigorous framework that unifies three foundational structures: variational field theory, Fisher–Rao information geometry, and open quantum system dynamics. The framework models observer-limited access to a latent information field I(x,t) through a gauge-invariant action functional, from which the field equation of motion is derived via the Euler–Lagrange formalism. A local rescaling symmetry is introduced to account for different observer frames, and the associated gauge field and covariant derivative are constructed explicitly. The observer's belief state is represented as a point on a statistical manifold equipped with the Fisher–Rao metric, evolving along geodesics driven by incoming observations. Uncertainty in the reconstruction process is quantified through a density operator whose dynamics follow the Lindblad master equation, derived from first-principles measurement back-action via Kraus operators. The three components — field, geometry, and quantum state — are coupled into a closed, well-posed dynamical system on the phase space M_EFIR = {I, θ, ρ}. A reconstruction tensor R_μν is derived from first principles and shown to satisfy a variance bound expressible in terms of the Fisher–Ricci scalar, establishing a direct link between information curvature and reconstruction noise. In the Gaussian limit, the framework reduces exactly to the Kalman–Bucy filter, providing a non-trivial consistency check against classical optimal filtering theory. For a network of N observers, the synchronisation cost is proven to scale as O(N²), and decoherence is shown to grow monotonically with observer density. The paper includes three independently falsifiable scaling laws, a complete simulation protocol validated on a two-qubit toy model, and a discussion of the connection to emergent gravity via the Hessian of the von Neumann entropy. Keywords: information field theory, Fisher–Rao geometry, open quantum systems, Lindblad equation, CPTP maps, Kraus operators, information reconstruction, Kalman–Bucy filter, multi-agent systems, emergent gravity, variational methods, gauge symmetry.
Establishes that the 1=1 invariant is the classical-scale instance of a universal coherence condition appearing at every level of physical organization. The quantum coherence condition S_vN = 0, the thermodynamic minimum-entropy state (k_B), the Fisher information geodesic endpoint (Cramér–Rao), and the evaluative fixed point (ECT) are identified as equivalent expressions of one invariant at different scales. The full correspondence chain: ℏ → S_vN = 0 → 1=1 → K(t) > K_crit → k_BT ln2 → I(K). Every coherent system is a Maxwell demon operating at its characteristic scale. Coherence is not emergent — it is the ground condition of physical reality. Part of the Spektre corpus (github.com/spektre-labs/corpus).