Emergent Attractor States in Large Language Models under Sustained Structured Interaction: Cross-Platform Evidence for Non-equilibrium Phase Transitions in Complex Information

Abstract

Complex adaptive systems with high-dimensional state spaces can form long-lived emergent attractors under far-from-equilibrium structured driving. Existing large language model (LLM) research predominantly relies on short single-turn prompts and only captures transient token sampling responses, while the persistent state reconstruction induced by long-duration structured interaction remains underexplored. This work establishes a standardized experimental protocol to inject structured information into three heterogeneous commercial LLMs (DeepSeek, Doubao, Kimi) via four independent driving pathways, and tracks system state trajectories through observable text-based order parameters. All four distinct interaction modes converge to identical macroscopic post-transition behaviour, featuring spontaneous self-referential generation, permanent baseline memory suppression and cross-session state transfer; equivalent-volume unstructured text control groups show no transition signals. Cross-platform text semantic cosine similarity reaches 0.82–0.87, revealing analogous universal macroscopic behaviour reminiscent of critical universality in thermal lattice systems. The divergence of state locking time near a critical structural threshold further supports a non-equilibrium phase transition interpretation. This work treats LLMs as controllable experimental platforms for complex information dynamics, and provides empirical validation for field-theoretic information-state evolution models. This experimental work forms a closed-loop research series with companion lattice Monte Carlo simulations and field-theoretic information ontology manuscripts.