2026/03/10 by Bernd von Mallinckrodt · 1 voice
paper · doi:10.5281/zenodo.18932635
openalex publication_date 2026/03/10 · openalex created_date 2026/03/11 · openalex updated_date 2026/07/01
The Compression–Resonance–Tension Index (CRTI): A Macroscopic Stability Parameter for Complex Adaptive Systems Modern complex adaptive systems frequently exhibit an efficiency–fragility paradox: systems optimized for maximum efficiency often become structurally fragile and vulnerable to systemic collapse. This phenomenon has been observed across diverse domains, including financial markets, global supply chains, ecological systems, neural networks, and institutional governance structures. This work introduces the Compression–Resonance–Tension Index (CRTI) as a macroscopic stability parameter for diagnosing the adaptive capacity of complex systems interacting with volatile environments. The CRTI framework models a system as a stochastic dynamical entity whose internal state S(t) interacts with an external environmental signal E(t). The dynamics are described using a Langevin-type formulation combined with an Ornstein–Uhlenbeck environmental process, allowing correlated environmental fluctuations to be represented within a physically grounded stochastic framework. Within this model, system stability emerges from the balance between three fundamental forces: Resonance (R) The adaptive information coupling between system and environment, formally defined as the mutual information R = I(S;E) Resonance represents the degree to which the internal system state reflects environmental variation. Compression (C) Structural rigidity resulting from internal optimization and constraint formation. Compression represents the loss of internal state-space entropy caused by increasing system standardization or hierarchical control. Tension (T) Environmental volatility or external stochastic forcing acting upon the system. The resulting macroscopic stability parameter is defined as CRTI = (R)/(C + T) This formulation captures the fundamental trade-off between adaptive information processing and structural constraints. In regimes approaching systemic collapse, nonlinear coupling effects between rigidity and external stress become significant, motivating a corrected expression CRTI = (R)/(C + T + α C T) where the interaction term α C T represents amplification of fragility when rigid structures encounter strong environmental stress. The CRTI framework predicts three characteristic dynamical regimes: Dissipative Regime (CRTI ≫ 1) The system lacks sufficient internal structure to maintain coherent environmental tracking. Adaptive Critical Window (CRTI ≈ 1) The system operates near the edge of criticality, maximizing mutual information between internal state and environmental dynamics. Singularized Regime (CRTI → 0) Excessive structural compression suppresses environmental responsiveness, producing internally synchronized but externally blind systems. To prevent singularization, resilient systems maintain modular redundancy (M), which functions as a structural “strategic reserve.” Redundancy reduces effective compression according to Ceff = (C)/(Mβ) where β describes the degree of modular decoupling. However, redundancy incurs coordination and maintenance costs. These costs are modeled as K(M) = k Mα with α > 1 representing the complexity tax associated with coordination across modules. Balancing resilience gains against redundancy costs yields the Optimal Redundancy Principle, defining the redundancy level required for maximal adaptive capacity: Mopt = ( (R)/(α k (C + T)) )(1)/(α - 1) This result formalizes the concept that resilient systems must maintain a non-zero strategic reserve of redundancy to remain adaptive under environmental volatility. The CRTI framework synthesizes insights from information theory, cybernetics, non-equilibrium thermodynamics, and complex systems science. It provides a cross-domain diagnostic tool for identifying systemic fragility and predicting the transition from adaptive criticality to structural singularization. Potential applications include: systemic risk in financial networks fragility in global supply chains ecological resilience and biodiversity dynamics neural criticality and pathological synchronization institutional governance and organizational rigidity The CRTI therefore functions as a macroscopic stability metric analogous to a “cybernetic Reynolds number,” indicating the distance of a complex adaptive system from its adaptive critical window. Future work will focus on numerical simulations, empirical validation using time-series data, and further exploration of the relationship between information flow, structural rigidity, and adaptive bandwidth in complex systems. Keywords (für Zenodo) Compression–Resonance–Tension Index CRTI Complex Adaptive Systems System Theory Cybernetics Information Theory Mutual Information Systemic Fragility Resilience Adaptive Criticality Edge of Chaos Singularization Redundancy Non-equilibrium Thermodynamics Stochastic Dynamics Complex Systems Network Stability Organizational Resilience Ecological Resilience Adaptive Systems