Coherence Loss in Long-Context Language Models as a Threshold Instability: A Plasma-Physics Analogy and a Feedback-Control Proposal
Large language models lose coherence over long reasoning chains and long contexts: accuracy degrades with input length well inside the nominal context window, per-step errors compound, and the end state is often a fluent contradiction of the model's own earlier statements. This note draws a structural analogy between that failure and a well-characterized instability in magnetized plasmas. In resistive magnetohydrodynamics the Lundquist number S = L·v_A/η is the ratio of the resistive-diffusion time to the dynamical (Alfvén) time; at large S, thin current sheets are unstable to the plasmoid instability and the magnetic topology reorganizes impulsively rather than smoothly. In tokamaks the corresponding tearing modes are suppressed by measured feedback, not by making the plasma more resistive. We propose an analogous dimensionless ratio for a reasoning chain, the coherence number Λ = n·ε·(1 − c), the expected number of uncaught errors in a chain of n steps with per-step error rate ε and per-step catch probability c of an external verifier; we state three falsifiable hypotheses that the analogy suggests, one of which (a collective threshold steeper than the independent-error baseline 1 − e^(−Λ)) would distinguish the analogy from a purely statistical account; and we specify a closed-loop verification controller, a proportional–derivative law acting on a measured inconsistency signal, together with a matched-budget protocol for testing it. We are explicit about scope: this is an analogy and not an isomorphism, no mapping between the plasma equations and transformer inference is claimed, no experimental result is reported, and the plasma side is motivational rather than load-bearing. Version 2 (6 September 2026) supersedes the December 2025 draft circulated as "The Viriato Protocol"; that draft's claims of isomorphism and of experimental validation are withdrawn.