2026/03/23 by Bernd von Mallinckrodt · 1 voice
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19181937
openalex publication_date 2026/03/23 · openalex created_date 2026/03/24 · openalex updated_date 2026/07/01
This preprint presents a controlled synthetic evaluation of the Compression–Response Thermodynamic Index (CRTI), a structural diagnostic framework for detecting instability in complex systems, in comparison to classical early warning signals (EWS) derived from critical slowing down theory. CRTI defines a viability index T = R / Φ, where Φ quantifies structural compression via the effective rank of the covariance matrix, and R captures adaptive response capacity via the dominant relaxation eigenvalue. The framework is evaluated in a multivariate Ornstein–Uhlenbeck (OU) system under three mechanistically distinct regimes: (A) endogenous compression through increasing inter-component coupling, (B) exogenous shock without prior structural buildup, and (C) an attempted variance-conserving compression scenario. The primary result is negative for the linear stochastic case: classical EWS (variance and lag-1 autocorrelation) consistently detect instability earlier than CRTI, with a median lead of 34–36 simulation steps in Regime A. In Regime B, neither CRTI nor EWS provide advance warning, consistent with mechanism-dependent expectations. Regime C reveals a structural constraint of the OU model class, demonstrating that covariance concentration and scalar variance cannot be decoupled under linear coupling. These findings clarify CRTI as a structural diagnostic rather than a classical leading indicator. The results highlight a fundamental distinction between amplitude-based and structure-based signals and motivate further investigation in nonlinear and network-driven systems where this distinction may become operationally relevant. early warning signals critical transitions structural compression Ornstein-Uhlenbeck processes covariance analysis complex systems regime shifts CRTI