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2026
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| Online Access: | https://doi.org/10.5281/zenodo.18878038 |
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| author | Moser, Pascal |
| author_facet | Moser, Pascal |
| contents | <p>We develop a unified statistical-mechanical framework in which information creation—the pro<br>gressive reduction of Shannon entropy through iterative correlation detection—is identified as the<br>fundamental mechanism underlying emergent collective behavior in networks of nonlinear threshold<br>elements. The framework rests on three interlocking structures: (i) a quasi-static information<br>creation model C(x) = [1 + e−k(x−x0)]−1 whose sigmoid form is derived from Kullback–Leibler<br>divergence minimization and free-energy reduction under a prediction-error learning rule; (ii) an ex<br>tended Boltzmann Transport Equation (BTE) in which the classical Stosshypothese is replaced by a<br>correlation-dependent scattering rate W(ω1,ω2,t) = W0(ω1,ω2)[1+ξcorr(t)], capturing the progres<br>sive buildup of correlations between nonlinear scattering events; and (iii) a mode-dependent Relax<br>ation Time Approximation (RTAcorr) that retains spectral structure lost by the standard single-τ<br>approximation. The extended BTE yields a self-consistent eigenvalue equation whose solutions Ωn<br>are the collective mode frequencies (alpha, beta, gamma oscillations in the neural realization). At<br>the critical threshold C(ωF) = 0.5 — the inflection point of the sigmoid and simultaneously the<br>Fermi level of the equilibrium occupation — the molecular-chaos assumption breaks down, correlated<br>scattering drives the distribution function away from its Fermi–Dirac baseline, and Frohlich-type<br>collective oscillations emerge as sharp spectral peaks in the power spectral density. We provide<br>a precise mathematical definition of emergence as this critical transition, show that it constitutes<br>a second-order phase transition with universal critical exponents independent of the microscopic<br>substrate, and demonstrate that the framework applies equally to neural populations, collective an<br>imal behavior, and any other network satisfying three minimal conditions: threshold nonlinearity of<br>components, iterative correlation buildup, and finite effective temperature T > 0. The single most<br>important empirical prediction concerns the spectral signature at the critical developmental inflec<br>tion point: a sudden appearance of spectral peaks in the EEG power spectral density, decreased<br>spectral entropy, and increased coherence time. We further prove that complete self-knowledge<br>C = 1.0 is structurally impossible—a mathematical consequence of G¨odelian self-reference, ther<br>modynamic noise at T > 0, and measurement-theoretic self-modification—establishing epistemic<br>humility as a necessary feature of any self-modeling system operating at finite temperature</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18878038 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Information Creation as a Universal Phase Transition: A Boltzmann Transport Framework for Emergent Collective Dynamics in Nonlinear Threshold Networks Moser, Pascal <p>We develop a unified statistical-mechanical framework in which information creation—the pro<br>gressive reduction of Shannon entropy through iterative correlation detection—is identified as the<br>fundamental mechanism underlying emergent collective behavior in networks of nonlinear threshold<br>elements. The framework rests on three interlocking structures: (i) a quasi-static information<br>creation model C(x) = [1 + e−k(x−x0)]−1 whose sigmoid form is derived from Kullback–Leibler<br>divergence minimization and free-energy reduction under a prediction-error learning rule; (ii) an ex<br>tended Boltzmann Transport Equation (BTE) in which the classical Stosshypothese is replaced by a<br>correlation-dependent scattering rate W(ω1,ω2,t) = W0(ω1,ω2)[1+ξcorr(t)], capturing the progres<br>sive buildup of correlations between nonlinear scattering events; and (iii) a mode-dependent Relax<br>ation Time Approximation (RTAcorr) that retains spectral structure lost by the standard single-τ<br>approximation. The extended BTE yields a self-consistent eigenvalue equation whose solutions Ωn<br>are the collective mode frequencies (alpha, beta, gamma oscillations in the neural realization). At<br>the critical threshold C(ωF) = 0.5 — the inflection point of the sigmoid and simultaneously the<br>Fermi level of the equilibrium occupation — the molecular-chaos assumption breaks down, correlated<br>scattering drives the distribution function away from its Fermi–Dirac baseline, and Frohlich-type<br>collective oscillations emerge as sharp spectral peaks in the power spectral density. We provide<br>a precise mathematical definition of emergence as this critical transition, show that it constitutes<br>a second-order phase transition with universal critical exponents independent of the microscopic<br>substrate, and demonstrate that the framework applies equally to neural populations, collective an<br>imal behavior, and any other network satisfying three minimal conditions: threshold nonlinearity of<br>components, iterative correlation buildup, and finite effective temperature T > 0. The single most<br>important empirical prediction concerns the spectral signature at the critical developmental inflec<br>tion point: a sudden appearance of spectral peaks in the EEG power spectral density, decreased<br>spectral entropy, and increased coherence time. We further prove that complete self-knowledge<br>C = 1.0 is structurally impossible—a mathematical consequence of G¨odelian self-reference, ther<br>modynamic noise at T > 0, and measurement-theoretic self-modification—establishing epistemic<br>humility as a necessary feature of any self-modeling system operating at finite temperature</p> |
| title | Information Creation as a Universal Phase Transition: A Boltzmann Transport Framework for Emergent Collective Dynamics in Nonlinear Threshold Networks |
| url | https://doi.org/10.5281/zenodo.18878038 |