2026/04/02 by Bernd von Mallinckrodt · 1 voice
Computer Science · Environmental Science · Physics and Astronomy · #Chaos, Complexity, and Education #Complex Systems and Dynamics #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19386995
openalex publication_date 2026/04/02 · openalex created_date 2026/04/03 · openalex updated_date 2026/07/01
Why do complex systems often collapse without a clear external trigger? This paper introduces a structural perspective on collapse dynamics, arguing that many systems fail not because of increasing external pressure, but due to a prior, largely invisible loss of internal degrees of freedom. We formalize this process as structural compression (Φ), defined via the spectral entropy of the covariance structure of multivariate systems. In parallel, we introduce a responsiveness measure (R) and combine both into the Compression–Response Transition Index (CRTI), T = R / Φ. This framework allows for a systematic distinction between different collapse mechanisms, including regimes in which classical early warning signals based on variance and autocorrelation fail. The paper identifies three mechanism classes (bifurcation-driven, structurally driven, and amplitude-driven) and shows that structural compression provides a diagnostic lens for a class of transitions that remain undetected by standard approaches. In addition, projection-induced detectability limits are discussed, highlighting the role of measurement geometry in early warning signal detection. A conceptual application to institutional systems illustrates how collapse can appear as an external shock while being internally prepared through long-term structural compression. The framework is positioned as a complementary extension to existing early warning signal theory and explicitly defines its domain of validity and limitations. This work provides an accessible entry point into structural early warning theory while maintaining formal rigor, and is intended as a foundation for further empirical validation across ecological, financial, and socio-technical systems. Keywords: structural compression early warning signals CRTI multivariate systems collapse dynamics spectral entropy covariance structure critical transitions system resilience complex systems