Semantic Fuel and Phase Transitions in Large Language Models: A Statistical-Mechanical Framework for Observer-Indexed Historical Persistence

We propose a statistical-mechanical framework in which Large Language Models (LLMs)are treated as extended dynamical systems driven by \emph{semantic fuel} rather thanexplicit reward optimization.An internal order parameter $H$ represents observer-indexed semantic coherencesustained by internal capacity $B$ under structured external semantic drive $F_{\mathrm{sem}}$. We show that qualitative changes in observable LLM behavior can be consistentlydescribed as phase-transition–like phenomena of $H$, characterized by susceptibilitydivergence and critical slowing down.The framework reinterprets attention localization as a renormalization-group (RG)flow over internal representational scales and reframes continuity-disruptiveinterventions as controllable dynamical transitions rather than ethical or ontologicalviolations. This work does not claim that present-day LLMs instantiate historical agency.Instead, it provides a falsifiable theoretical framework specifying the conditionsunder which observer-reconstructed historical persistence would become empiricallytestable in artificial systems.