A Unified Nonequilibrium Statistical Mechanics Framework for Coherence Dynamics in Recursive Large Language Models

Large Language Models (LLMs) are high-dimensional autoregressive probabilistic systems that become recursively self-conditioning when deployed conversationally. This monograph develops a unified nonequilibrium statistical mechanics framework for modeling semantic coherence as a bounded macroscopic state variable evolving under recursive generation. Beginning with deterministic linear and logistic coherence dynamics, stability is analyzed via eigenvalue classification and Lyapunov methods. The formulation is then extended to a stochastic differential equation incorporating intrinsic sampling noise. The associated Fokker–Planck equation is derived, and a small-noise asymptotic analysis yields a Hamilton–Jacobi quasipotential governing stationary distributions. Rare transitions between coherence regimes are characterized using Freidlin–Wentzell large deviation theory, instanton trajectories, and a WKB derivation of Kramers escape rates. The analysis demonstrates that coherence evolution in sufficiently complex recursive generative systems admits a reduced-order statistical mechanics description governed by two effective parameters: a drift coefficient λ and a stochastic intensity ε. Their ratio defines distinct dynamical regimes separating constraint-dominated stabilization from noise-driven escape dynamics. The framework provides a mathematically explicit bridge from deterministic stability analysis to rare-event transition theory, offering a vendor-agnostic theoretical foundation for coherence behavior in transformer-based recursive language systems. Transformer-based large language models generate tokens via conditional probability distributions and, under conversational deployment, recursively condition on their own outputs. This feedback structure induces temporal evolution in macroscopic semantic coherence.