Dynamic Epistemic Channels and the Collapse of Effective Information in Feedback Control

Classical Shannon theory treats channel capacity as a static guarantee: if 𝐶 exceeds the information rate a control task requires, reliable feedback is possible. We show this guarantee is insufficient in systems where information, once transmitted, must traverse a delay window during which the world continues to evolve. We introduce a dynamic extension of the Shannon channel in which transmission is governed by erasure 𝜀(𝑡), delay 𝜏 , and a windowed decorrelation integral Λ(𝑡, 𝜏 ) = ∫𝑡 𝑡−𝜏 𝜆(𝑠) 𝑑𝑠 — the accumulated epistemic drift over the delay window. We define effective information 𝐼effective(𝑡) = (1 −𝜀(𝑡))𝑒−Λ(𝑡,𝜏)𝐼 Shannon(𝑡) as the control-relevant rate, and prove the Dynamic Channel Collapse Theorem: 𝐼effective(𝑡) → 0 if and only if Λ(𝑡, 𝜏 ) → ∞, even when 𝜀(𝑡) is bounded away from 1 and 𝐼Shannon(𝑡) remains within sufficient Shannon capacity. We reinterpret this as an Epistemic Control Postulate: a feedback law’s actionable signal is its observation weighted by 𝐼effective(𝑡), so that closed-loop instability decomposes into two independent causes — classical controller failure, and epistemic channel collapse, which no redesign of the controller alone can repair. We connect this to Ashby’s variety bound as a temporal refinement (capacity vs. currency of information) and to autoregressive generation, where the framework yields a candidate formalization of hallucination as epistemic collapse under a fixed context window. We propose observable proxies for 𝜆(𝑡) and 𝜅(𝑡) via representation drift, Fisher information decay, and attention entropy, and outline an empirical protocol linking the theorem’s predictions to existing early-warning detection results. The central claim: capacity is a static property of transmission; control is a property of how much epistemic drift accumulates within the window a system is forced to act over — and bounded capacity does not prevent that window from becoming arbitrarily uninformative.