CRTI 2.5: A Nonlinear Information-Thermodynamic Model of Structural Compression, Feedback Permeability, and Adaptive Collapse

2026/03/01 by Bernd von Mallinckrodt · 1 voice

paper · doi:10.5281/zenodo.18823521

openalex publication_date 2026/03/01 · openalex created_date 2026/03/02 · openalex updated_date 2026/07/01

Abstract

CRTI 2.5 – Historical Development and Formalization The Compression–Resonance Thermodynamic Index (CRTI) originated as a conceptual diagnostic framework for identifying structural overcompression in complex adaptive systems. Earlier versions (CRTI 1.x–2.2) introduced the basic ratio structure between structural rigidity (R) and feedback permeability (Φ), proposing that systemic instability arises not from chaos, but from absolutized order combined with reduced feedback processing. CRTI 2.3 established an information-theoretic foundation by defining: Structural RigidityR = 1 - \fracH(S)H_max Feedback PermeabilityΦ = (I(E;S))/(H(E)) thereby grounding the model in Shannon entropy and mutual information. CRTI 2.4 introduced a coupled dynamical formulation, revealing that the purely linear two-variable system exhibits intrinsic saddle-type instability under strictly positive parameters. CRTI 2.5 represents the first fully dynamical three-variable formulation, incorporating: R (structural compression) Φ (environmental information transmission) Z (strategic reserve / adaptive buffer capacity) A key mathematical result documented in this preprint is that the linear 3-variable core remains generically unstable (a₀ < 0 under positive parameterization), making stable adaptive regimes impossible without bounded nonlinearities. Therefore, CRTI 2.5 introduces minimal nonlinear stabilization terms that enable: Locally stable adaptive equilibria Reserve-depletion-driven regime shifts Hysteresis under parameter sweeps Early-warning signal emergence (critical slowing down) The model synthesizes elements from: Information Theory (Shannon, Jaynes) Nonlinear Dynamics Resilience Theory (Holling) Critical Transition Theory (Scheffer et al.) Free Energy formalism (Friston, interpretative level) This document provides: Formal definitions Algebraic validation Stability analysis Corrected Routh–Hurwitz conditions Nonlinear stabilization framework Minimal simulation design CRTI 2.5 is intended as a theoretical preprint establishing mathematical coherence prior to empirical calibration in organizational, economic, or institutional systems. 🔑 15 Optimized Keywords (Zenodo-ready) complex adaptive systems nonlinear dynamics bifurcation theory tipping points critical transitions resilience modeling structural rigidity mutual information Shannon entropy information thermodynamics early warning signals hysteresis adaptive collapse dynamical systems phase transitions

Discussions

• If structural overcompression & adaptive collapse are nonlinear phase phenomena, shouldn’t we model them within a unified information-thermodynamic framework rather than isolated ratios? #CRTI2.5 for [bsky, 2 points, 0 comments]

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