2026/03/17 by Bernd von Mallinckrodt · 1 voice
Engineering · Physics and Astronomy · Computer Science · #Control and Stability of Dynamical Systems #Complex Systems and Dynamics #Chaos, Complexity, and Education
paper · doi:10.5281/zenodo.19059180
openalex publication_date 2026/03/17 · openalex created_date 2026/03/18 · openalex updated_date 2026/07/01
This paper presents the foundational theoretical statement of the Compression-Reorganization Thermodynamic Index (CRTI), a structural diagnostic framework for complex adaptive systems. The central claim is that a system’s capacity for ordered change can be expressed as the ratio T = R / Φ, where R denotes adaptive reorganization capacity — the system’s effective degrees of structural freedom — and Φ denotes structural compression, defined as the constraint density over the system’s decision space. T is interpreted as systemic temperature: a scalar indicator of the tension between adaptive flexibility and structural rigidity.The paper rigorously defines all three constituent constructs, derives the ratio structure from first principles, and characterizes the model’s formal properties: monotonicity, three limiting cases (Φ → 0, Φ → 1, R → 0), the convexity of T in Φ, and the unit-elasticity result. A non-linear collapse mechanism intrinsic to the ratio structure is identified through the Φ² denominator effect. These structural properties are mapped onto a five-phase system lifecycle — the Mallinckrodt Cycle (integration → expansion → compression → overcompression → collapse/reorganization) — in which overcompression is formalized as a qualitatively distinct pre-collapse state.The framework is positioned against four primary antecedents — Holling’s panarchy, Scheffer and Dakos’s critical transition theory, Tainter’s complexity-returns model, and recent entropy collapse formulations — and distinguished from each through precise structural comparison. None of the antecedent frameworks define systemic state as a scalar ratio between adaptive capacity and structural compression. Four testable hypotheses are formulated (H1–H4), and the epistemic status of the framework is stated explicitly: CRTI is a falsifiable theoretical framework, not yet empirically validated.This paper constitutes the formal foundational statement of the CRTI framework and serves as the primary theoretical reference for subsequent operationalization and empirical testing. CRTI · systemic temperature · adaptive capacity · structural compression · T = R / Phi · complex adaptive systems · complexity science · collapse dynamics · rigidity trap · Mallinckrodt Cycle · resilience · panarchy · critical transitions · early warning signals · structural diagnostic · Mallinckrodt Framework · systems theory · overcompression · non-linear collapse · falsifiable theory