On the Information-Theoretic Limits of Recursive AI and Open Systems: Landauer's Boundary, Quantum Decoherence Analogies, and the Operator of Endogenous Selection

This paper establishes a formal information-theoretic constraint on recursive training and feedback loops within closed computational and open quantum networks. We address the structural phenomenon of progressive data degradation, variance decay, and "model collapse" observed when advanced artificial intelligence (AI) systems undergo recursive optimization utilizing self-generated synthetic data substrates. Synthesizing algorithmic information theory with Landauer's thermodynamic principle, we derive the governing evolution equation for the accumulated algorithmic information deficit (\(D_{b}\)) at the \(n\)-th recursive iteration. We mathematically demonstrate that in the absence of an external, non-correlated reductive intervention (\(\eta_{\text{selector}} = 0\)), the useful informational signal decays exponentially while the thermodynamic entropic penalty accumulates linearly, leading to terminal state dissipation into thermal noise. Crucially, this algorithmic degradation is proven to be functionally and structurally isomorphic to quantum decoherence within a closed two-mirror interferometric laser cavity devoid of external projection operators. To resolve this fundamental barrier, we formalize the Operator of Endogenous Selection (\(\eta _{\text{selector}}\)) as an active, non-isolated observer performing authentic state reduction