Nonequilibrium Semantic Thermodynamics on Typed Graphs

We present a nonequilibrium thermodynamics of meaning on typed discourse graphs that turns coherence into measurable, controllable, and reproducible quantities. The state (𝑆,𝜎,𝑔𝑉,Θ)closes under a flux law 𝐵=𝜎∇𝑆and a free energy 𝐹=𝑈−Θ𝐻sem; coherence 𝜅and entropy production Σ̇serve as human-readable observables. We prove that 𝐹is a Lyapunov functional for the field dynamics (𝐹̇=−Θ Σ̇≤0), derive stability corridors, and show that Σ̇spikes act as early-warning signals of forthcoming drift. In the small-force regime we obtain a discrete Green–Kubo/FDT formula that identifies 𝜎from autocorrelations of the observable flux 𝐵, with finite-sample estimators and confidence bounds. We establish structure-invariance guarantees—Δ ⁣Fold≤𝐶1∥∇𝑆∥𝑊2 and boundary stability BS≥1−𝐶2∥∇𝑆∥2—with constants tied to a 𝜎-weighted Cheeger floor. To make claims auditable, SIP RFC-0001 specifies a deterministic, batch-invariant decode path (seed/version pins, run-card, byte-exact verifier). Experiments validate 𝜎on synthetic typed graphs and show, in RAG/long-context pipelines, that field regularization lowers Δ ⁣Fold, raises BS and 𝜅, and triggers timely Σ̇alarms; under load, RFC-0001 attains 100% cross-node reproducibility. We evaluate two preregistered predictions: smoothing ∥∇𝑆∥monotonically reduces Δ ⁣Fold, and Σ̇spikes forecast drift windows.