2026/02/24 by Bernd von Mallinckrodt · 1 voice
paper · doi:10.5281/zenodo.18756738
openalex publication_date 2026/02/24 · openalex created_date 2026/02/25 · openalex updated_date 2026/07/01
This publication introduces the Compression–Resonance Thermodynamic Index (CRTI) as a configurational state variable for analyzing phase transitions in over-compressed adaptive systems. The work formalizes a structural mechanism by which complex adaptive systems (CAS) undergo abrupt collapse despite apparently stable performance metrics. The framework is built upon three normalized macroscopic variables: exploitation (E), exploration (X), and resonance integrity (R). Systemic compression is defined as the ratio ΦR = E / X. The adaptive capacity of the system is expressed through the CRTI: CRTI(ΦR) = T(ΦR) = r(ΦR) / ΦR Resonance integrity r(ΦR) is modeled as a logistic attenuation function with a Structural Permeability Limit Φc. Under rising compression, this attenuation induces a non-linear loss of adaptive temperature. Analytical derivation of the susceptibility χ(ΦR) = | dT / dΦR | reveals the emergence of a Brittleness Window, defined by a local maximum in susceptibility near Φc. Within this window, marginal increases in compression produce disproportionate losses in adaptive capacity. Sensitivity analysis demonstrates that the structural hardness parameter k sharpens the phase transition without shifting the critical threshold Φc. Numerical mini-simulation confirms that high-compression regimes exhibit a cliff-like collapse of CRTI, whereas elastic regimes transition gradually and avoid entering the Brittleness Window. The model is intentionally domain-agnostic and non-normative. It does not predict specific institutional failures; rather, it establishes a geometric invariant of compression-driven adaptive systems. Calibration of Φc, k, and operational susceptibility thresholds is domain-dependent and requires empirical shock-response data. By reframing systemic fragility as a structural phase transition, this work contributes a compact analytical geometry for diagnosing latent brittleness in complex networks across socio-technical, biological, and organizational domains. Phase Transition Complex Adaptive Systems Over-Compression Exploitation–Exploration Trade-off Resonance Attenuation Structural Permeability Susceptibility Analysis Nonlinear Dynamics Critical Thresholds Logistic Attenuation Model Systemic Brittleness Adaptive Capacity Compression–Resonance Thermodynamic Index (CRTI) Statistical Mechanics of Social Systems Network Stability and Collapse