No Stationary Entropy-Production Attractor in Frozen de Sitter Wright–Fisher Coarsening: A Null Result Closing the σ→μ_D Route

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Authors: Arturo Cerezo
Cited by: 2

Abstract

We report a pre-registered null test (KS-B1) of the σ*→μ_D hypothesis within the Radial Coherential Dynamics (RCD) program: the conjecture that the stationary entropy-production rate of the sealed Allen–Cahn/Wright–Fisher kernel fixes the disformal coupling scale μ_D — the last remaining route by which that scale could be derived rather than calibrated. We measure the medium entropy production with a pathwise T-odd functional (Stratonovich midpoint), which, unlike Schnakenberg-type estimators, requires no stationary density and therefore evades the failure mode of an earlier attempt. We identify and remove a boundary-singularity artifact: with ~97% of lattice sites saturated, the raw estimator returns σ_raw ≈ −1.1e5 driven entirely by the 1/[C(1−C)] singularity; the active-site estimator collapses this by four orders of magnitude. In the frozen de Sitter regime (≥7 t_H, five seeds) we find σ_ss = 0.030 ± 0.152 in lattice units (2-SEM bound |σ_ss| < 0.33), suppressed by ≈2.0e3 relative to the active coarsening epoch (σ_act(1 t_H) ≈ +657), with an instrumental floor of order 1e−1 compatible with a decreasing O(dt)-like bias. A stationary state does exist in de Sitter — correcting an earlier non-existence claim — but it is an effective frozen equilibrium, not a positive-σ source. Within the sealed kernel and tested backgrounds, no positive stationary entropy-production attractor exists from which μ_D can be fixed. The σ*→μ_D route is closed in red; the only reopening requires a field–horizon noise bridge (Gibbons–Hawking-type sourcing), explicitly identified as Obstruction 1 and not derived here. Deposit contents: main preprint (PDF + Markdown source), standalone abstract, reproducibility checklist, figure plan, CITATION.cff, README, and the KS-B1 script chain with preserved console outputs (files.zip). Pre-registered gates, seeds, and parameters are documented in the checklist; verdict-logic corrections and executor autocorrections are recorded in Appendix B of the preprint.

Fields of Study & Subjects

Statistical Mechanics and Entropy Theoretical and Computational Physics Advanced Thermodynamics and Statistical Mechanics

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
11 June 2026
Language
EN
Document type
Preprint