Bernd von Mallinckrodt 🦋Structural Compression and Ada...
Structural Compression and Adaptive Capacity: A State-Space Generalization of the Ascendency–Overhead Framework
This paper introduces the Compression–Resonance Thermodynamic Index (CRTI) as a domain-general diagnostic for structural over-compression in complex adaptive systems. Building on Ulanowicz’s ascendency–overhead formalism, the framework is reformulated in a state-space and information-theoretic setting. Structural compression is defined as the reduction of effective state-space dimensionality, while adaptive reorganization capacity is quantified via the conditional entropy of reachable future states. The resulting index, CRTI = R/Φ, captures the balance between adaptive openness and accumulated structural constraint. Within ecological flow networks, an exact and invertible mapping to Ulanowicz’s relative ascendency is derived, establishing CRTI as a mathematically explicit generalization of the ascendency–overhead framework. Outside this domain, the relationship becomes structural-analogical, preserving the underlying information-theoretic logic while extending applicability to arbitrary complex systems. The framework introduces a trajectory-based diagnostic perspective: the time derivative d(CRTI)/dt < 0 is identified as an early-warning signal for progressive loss of adaptive capacity, preceding classical indicators such as critical slowing down. This enables the identification of a distinct failure regime, termed singularization, characterized by maximal structural compression and near-deterministic system dynamics. The CRTI is positioned not as a new collapse mechanism, but as a unified, state-space based formalization of a widely observed phenomenon: the loss of accessible future configurations under increasing constraint. The approach integrates concepts from information theory, cybernetics, and resilience theory, and is applicable across ecological, organizational, and socio-technical systems. Limitations include the domain-restricted exactness of the mapping to flow-based formalisms, the dependence on state-space specification, and the need for empirical calibration of diagnostic thresholds. Future work includes empirical validation using ecological network data, organizational time series, and stochastic dynamical systems. Preprint version. This work is part of the Mallinckrodt Framework (V3.x) research series. complex adaptive systems structural compression adaptive capacity CRTI information theory ascendency overhead Ulanowicz cybernetics Ashby requisite variety entropy state-space dynamics conditional entropy mutual information early warning signals system collapse resilience theory singularization
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