Dynamical Observability in Complex Systems: A Negative Result on Temporal Mutual Information as a Structural Diagnostic

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Abstract

Abstract Temporal mutual information, O(τ ) = I(Xt; Yt+τ )/H(Xt), measures what fraction of a system’s hidden state is recoverable from its output at lag τ. We test this metric on AI hidden states, agent-based model aggregates, 15 US macroeconomic indicators (1950–2026), a calibrated labor market ABM, transfer entropy networks, and partial information decomposition. In every setting the metric fails to produce insights that cheaper, established tools cannot. When source and target coincide, O(τ ) is autocorrelation in disguise; when they differ, the resulting patterns are model-specific or reproducible by Granger causality. Even transfer entropy and PID, which condition on confounders and decompose shared information, add nothing for macroeconomic monthly data, because joint histogram estimation collapses under the curse of dimensionality. The negative result is not that information theory is wrong about these systems, but that it offers no analytical advantage over the tools economists already use.