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Stochastic Rupture via State-Dependent Rate Instability in the Reaction-Diffusion Field Theory

GUILHERME ZAMBUZI

Published May 17, 2026• 0 citations
Publisher

Abstract

We propose a stochastic rupture mechanism for reaction-diffusion systems based on a state-dependent relaxation rate Γeff(χ) = Γ0 −λχ, which vanishes at the critical amplitude χc = Γ0/λ. This modification is exactly equivalent to a renormalization of the nonlinear coupling in the Langevin equation, preserving locality and the full Martin–Siggia–Rose–Janssen–De Dominicis (MSRJD) formalism. We identify the scalar field χ with the local informational saturation ratio χ = SvN/(η IBek) of the Stochastic Rupture (SR) framework [1], where SvN is the local von Neumann entropy and IBek is the Bekenstein bound of the enclosing causal-diamond region. Under the physically motivated condition α = λ/2, we derive—rather than postulate—the satu- ration feedback function F(χ) = (1 − χ) −1 as a direct consequence of the divergence of the zero-momentum field-fluctuation variance at the critical point. We further derive the homogeneous mean-field dynamics χ(t) and recover the rupture-time estimate τSR ∼ η/γ0 for nanoparticle superpositions. An analogy with overclocking and thermal throttling in computational processors provides physical intuition, in- cluding a speculative interpretation of quantum tunneling as time dilation between dynamically distinct regimes. A conceptual experiment using optically levitated nanoparticles to discriminate this framework from standard decoherence is proposed. The renormalization group analysis of this theory and the determination of its universality class are reserved for a companion work.

DOI
10.5281/zenodo.20262210

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The Stochastic Rupture (SR) framework for objective wave-function collapse is reformulated as a non-equilibrium statistical field theory using the Martin–Siggia–Rose–Janssen–De Domini- cis (MSRJD) path-integral formalism. The SR Langevin equation for the holographic saturation field χ admits an exact mapping to an MSRJD action with a cubic nonlinearity. Dimensional analysis yields an upper critical dimension dc = 4 and a dynamic exponent z = 2. In d = 3 a one-loop renormalization group (RG) analysis reveals a non-trivial infrared-stable fixed point at dimensionless coupling g ∗ = π (exact, of geometric origin). At this fixed point the satu- ration parameter η—previously phenomenological in SR v14–v15 with the empirical window 3 × 10−2 ≲ η ≲ 1—emerges as the expectation value ⟨χ⟩|g ∗ , not a free input. A specific prediction, contingent on the explicit evaluation of the source-renormalization diagram coefficient cS, is η = 2/3 (verified to machine precision under the stated condition). All assumptions are stated explicitly and open theoretical problems are listed
The Stochastic Rupture (SR) framework for objective wave-function collapse is reformulated as a non-equilibrium statistical field theory using the Martin–Siggia–Rose–Janssen–De Domini- cis (MSRJD) path-integral formalism. The SR Langevin equation for the holographic saturation field χ admits an exact mapping to an MSRJD action with a cubic nonlinearity. Dimensional analysis yields an upper critical dimension dc = 4 and a dynamic exponent z = 2. In d = 3 a one-loop renormalization group (RG) analysis reveals a non-trivial infrared-stable fixed point at dimensionless coupling g ∗ = π (exact, of geometric origin). At this fixed point the saturation parameter η—previously phenomenological in SR v14–v15 with the empirical window 3 × 10−2 ≲ η ≲ 1—emerges as the expectation value ⟨χ⟩|g ∗ , not a free input. A specific prediction, contingent on the explicit evaluation of the source-renormalization diagram coefficient cS, is η = 2/3 (verified to machine precision under the stated condition). All assumptions are stated explicitly and open theoretical problems are listed.
Stochastic Rupture (SR) proposes that objective wavefunction collapse is triggered when local von Neumann entropy saturates a fraction eta of the holographic Bousso bound on causal-diamond surfaces. The SR network is concretely realized as a simple cubic lattice — square holographic sheets stacked at Planck-scale intervals — whose exact Laplacian spectrum derives the dimensional flow d s: 2 ( UV, holographic ) to 3 ( stacking ) to 4 ( Lorentzian, open ) without free parameters. The framework has two logically independent sectors. The collapse sector is self-contained and makes parameter-free falsifiable predictions. The general SR decoherence rate Gamma SR = Gm squared /(4 h bar sigma x squared ) produces a sigma x to the minus 2 scaling that discriminates SR from CSL (sigma x to the minus 3) and Diósi–Penrose (flat), independently of any free parameters; the definitive test is at MAQRO (10 to the 9–10 to the 10 amu). For GHZ/Bell states on NISQ hardware, the SR-native prediction is tau Bell / tau GHZ is similar to N squared, with a finite-size correction: reliable collapse onset at N stable is approximately equal to 1.25/(1 minus eta ) rather than the theoretical threshold 1/(1 minus eta ). The geometric sector — Newton's law, Einstein equations, spin-2 graviton — is conditional on the IR limit d s to 4 and is presented explicitly as such. Two new structural results reduce the number of free parameters. The bond-percolation threshold of the simple cubic lattice, p c = 0.2488, matches the cosmological structure-suppression parameter e 0 = 0.249 plus or minus 0.035 to within 0.1 %, linking the connectivity transition of the SR network to the S8 tension without a free fit. The restoration rate lambda q, previously unconstrained, is shown to satisfy lambda q/ gamma 0 is approximately equal to 1/ the square root of pi through a three-step geometric argument: vibrating holographic sheets drive saturation fluctuations to the 2D square interface critical point p c=1/2; Bernoulli variance at criticality gives sigma = the square root of 3 /2; three independent propagation channels in 3D then fix lambda q/ gamma 0 = C/ the square root of pi with C is approximately equal to 0.995. The remaining open step — showing the SR interface dynamics belongs to the Model A universality class with additive noise — reduces to a single one-loop RG calculation. The framework makes fourteen falsifiable predictions spanning NISQ processors, MAQRO, LISA, and Euclid, explicitly distinguishing derived results from calibrated parameters and open problems.
We propose a falsifiable model where proper time emerges from a finite local sampling rate N(x) = Ilocal/IPlanck, and wavefunction collapse occurs when a branch’sinformation exceeds the Bekenstein bound. The model recovers General Relativity inthe low-entropy limit and predicts anomalous decoherence for massive superpositionswith SvN ≳ 0.1 · IBek. A concrete experimental test is proposed using next-generationmatter-wave interferometers, along with a near-term laboratory suggestion using optomechanical platforms.
The Stochastic Rupture (SR) framework postulates that wavefunction collapse is an informational phase transition triggered by the saturation of local holographic entropy bounds. A central corollary of this framework is the emergence of proper time as a function of local informational occupancy: dτ = dt, IPlanck χ, η, Acausal . (1)While previous analyses focused primarily on the collapse regime (χ → 1), this work explores the opposite limit (χ → 0), characteristic of microscopic quantum systems. We propose that the extreme temporal acceleration associated with low informational saturation provides a physical explanation for quantum delocalization. In this picture, the wavefunction describes a temporally generated ensemble of rapidly iterated configurations within a coarse external time slice. Apparent spatial superposition therefore emerges as a relativistic asynchrony between informational proper time and macroscopic coordinate time.
We present numerical evidence for the structural predictions of the Stochastic Rupture (SR) framework [1], focusing on three independent simulation programs. First, direct computation of modular variance Var(Jz) confirms the GHZ/Bell scaling theorem: ISR[GHZN ] = N2/4 and ISR[BellN/2] = N/2, giving τBell/τGHZ ∼ N/2 for systems of equal total mass. Second, percolation simulations on entanglement networks reveal a universal scaling law for the Erd˝os– R´enyi topology: pc ·N = 1+√η, confirmed numerically for N = 50 to N = 1000 and converging to the theoretical value 1+√η as N → ∞. Third, these results are shown to depend on network topology in a structured way—reflecting the bond percolation critical exponents of each graph class—and are robust to random site defects up to 50%, with the universal form surviving after replacing N with Neff. Connections to the superfluid 4He λ-transition and to measurementinduced phase transitions in random quantum circuits are identified as consistency anchors, providing plausibility support without constituting independent tests of SR. The simulations suggest that η is experimentally calibrable from the entanglement percolation threshold of a physical platform, provided the underlying network topology is known.