Nonlinear Emergent Causal Structure from Bures Gradient Flows: Numerical Evidence for a Stable Hyperbolic Attractor
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| Natura: | Recurso digital |
| Lingua: | inglese |
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2026
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| _version_ | 1866901898224730112 |
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| author | Rusishvili, Mikheil |
| author_facet | Rusishvili, Mikheil |
| contents | <p>The Emergent Spacetime program (Informational Geometry of Emergent Spacetime – IGES) has shown that the linearized Information Open-systems Flow (IOF) on the Bures manifold of density operators projects to a symmetric hyperbolic hydrodynamic system whose characteristic cone is exactly Lorentzian. This established that spacetime causal structure can emerge from quantum information degradation, but only in the tangent-space approximation. In this work, we address the principal remaining gap: we provide strong numerical evidence for a Nonlinear Emergent Causal Structure Scenario, supporting the conclusion that an effective hyperbolic causal cone acts as a dynamically stable attractor of the full, nonlinear IOF dynamics. We implement a complete numerical simulation of two coupled qubits with dephasing on a 1D lattice, evolving the exact IOF on the 15-dimensional Bures manifold. At each time step we extract the Bures Hessian of the information degradation functional, construct the dynamic spectral gap ∆(t), compute the nonlinear Schur complement Keff(t), and measure the instantaneous cone deviation δ(t) ≡ supk |ω 2 (t, k) − c 2 s(t)k 2 |. </p> <p>We find that: (1) the fast/slow mode separation persists globally; (2) the spectral gap remains strictly positive, ∆(t) ≥ ∆0 > 0; (3) the effective reduced generator Keff(t) remains symmetric in the Bures metric to machine precision; (4) the cone deviation δ(t) decays as e −∆t , falling below 10−4 after a few gap times. These results provide significant evidence that the emergent hyperbolic causal structure is not a linear artifact – the effective causal cone is a robust attractor of the full gradient flow. This nonlinear stability suggests compatibility with Jacobson-type thermodynamic gravity scenarios. The complete simulation code and diagnostic data are provided as supplemental material. </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20152184 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Nonlinear Emergent Causal Structure from Bures Gradient Flows: Numerical Evidence for a Stable Hyperbolic Attractor Rusishvili, Mikheil Emergent Spacetime Informational Geometry Information Geometry Quantum Information Geometry Emergent Gravity Lorentzian Geometry Thermodynamic Gravity Emergent Causal Structure Hyperbolic Attractor Nonlinear Dynamics Gradient Flow Bures Geometry Bures Manifold Information-Theoretic Physics Quantum Statistical Geometry Emergent Lorentz Symmetry Spacetime Emergence Dynamical Causal Cone Information Degradation Geometric Quantum Dynamics <p>The Emergent Spacetime program (Informational Geometry of Emergent Spacetime – IGES) has shown that the linearized Information Open-systems Flow (IOF) on the Bures manifold of density operators projects to a symmetric hyperbolic hydrodynamic system whose characteristic cone is exactly Lorentzian. This established that spacetime causal structure can emerge from quantum information degradation, but only in the tangent-space approximation. In this work, we address the principal remaining gap: we provide strong numerical evidence for a Nonlinear Emergent Causal Structure Scenario, supporting the conclusion that an effective hyperbolic causal cone acts as a dynamically stable attractor of the full, nonlinear IOF dynamics. We implement a complete numerical simulation of two coupled qubits with dephasing on a 1D lattice, evolving the exact IOF on the 15-dimensional Bures manifold. At each time step we extract the Bures Hessian of the information degradation functional, construct the dynamic spectral gap ∆(t), compute the nonlinear Schur complement Keff(t), and measure the instantaneous cone deviation δ(t) ≡ supk |ω 2 (t, k) − c 2 s(t)k 2 |. </p> <p>We find that: (1) the fast/slow mode separation persists globally; (2) the spectral gap remains strictly positive, ∆(t) ≥ ∆0 > 0; (3) the effective reduced generator Keff(t) remains symmetric in the Bures metric to machine precision; (4) the cone deviation δ(t) decays as e −∆t , falling below 10−4 after a few gap times. These results provide significant evidence that the emergent hyperbolic causal structure is not a linear artifact – the effective causal cone is a robust attractor of the full gradient flow. This nonlinear stability suggests compatibility with Jacobson-type thermodynamic gravity scenarios. The complete simulation code and diagnostic data are provided as supplemental material. </p> |
| title | Nonlinear Emergent Causal Structure from Bures Gradient Flows: Numerical Evidence for a Stable Hyperbolic Attractor |
| topic | Emergent Spacetime Informational Geometry Information Geometry Quantum Information Geometry Emergent Gravity Lorentzian Geometry Thermodynamic Gravity Emergent Causal Structure Hyperbolic Attractor Nonlinear Dynamics Gradient Flow Bures Geometry Bures Manifold Information-Theoretic Physics Quantum Statistical Geometry Emergent Lorentz Symmetry Spacetime Emergence Dynamical Causal Cone Information Degradation Geometric Quantum Dynamics |
| url | https://doi.org/10.5281/zenodo.20152184 |