2026/04/18 by Bernd von Mallinckrodt · 1 voice
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Statistical Mechanics and Entropy #Target Tracking and Data Fusion in Sensor Networks
paper · doi:10.5281/zenodo.19645383
openalex publication_date 2026/04/18 · openalex created_date 2026/04/19 · openalex updated_date 2026/07/01
This manuscript establishes a necessary-and-sufficient condition under which spectral functionals of the observed covariance matrix—such as effective rank and spectral entropy—provide information beyond scalar second-order statistics, including rolling variance and lag-1 autocorrelation. The result is formulated as a property of the system–observation pair rather than of the system alone, demonstrating that structural information is representation-dependent. The analysis is confined to stationary linear Gaussian stochastic differential equations under linear observation and is supported by an analytically transparent Ornstein–Uhlenbeck counterexample and a Lyapunov-based dynamical extension. The scope is explicitly bounded. No universality is claimed, no new indicator is proposed, and no superiority over classical early-warning signals is asserted. The contribution is delimitative: it specifies when structural diagnostics can, and cannot, add independent information in the stated regime. This deposit provides a stable, citable reference version. Simulation code implementing the Euler–Maruyama integration, rolling covariance estimation, and Marchenko–Pastur correction is available from the author on request. Keywords structural observability, covariance structure, effective rank, spectral entropy, stochastic systems, linear Gaussian SDE, early-warning signals, Lyapunov equation, Ornstein–Uhlenbeck process, random matrix theory, Marchenko–Pastur, multivariate time series