Semantic Thermodynamics: A Formal Model for Coherence Dynamics under Drift

Semantic Thermodynamics introduces a formal theoretical framework describing how semantic coherence behaves as an energetic quantity within iterative transformation systems. The paper models coherence as a structured potential field, semantic drift as thermodynamic pressure, and convergence as gradient descent over a semantic energy function (semantic Hamiltonian):

H(s) = α·G(s) + β·I(s) + γ·U(s) − δ·Ev(s)

The framework shows that coherence loss follows entropy-like dynamics, and that self-validation naturally emerges when a system minimizes semantic energy under continuous drift. Using the convergence equation

dH/dt = −λ·H + δd

the model provides explicit mathematical conditions for stability, bounded drift, and equilibrium.

This work is the theoretical counterpart to the author’s companion paper “Self-Validating Systems: Convergence Governance” (2025). Together, they define both the governance architecture and the physical substrate required for reliable, auditable, self-correcting AI-assisted transformation pipelines.

The paper includes a structured summary of independent empirical validation (Appendix C), demonstrating exponential energy decay, Gibbs-like equilibrium behavior, temperature-dependent sampling dynamics, and convergence across large semantic state spaces. Full empirical results will be published separately in a dedicated methodological paper.

This preprint establishes the foundational theory for semantic energy models, convergence guarantees, and thermodynamic reasoning over meaning. It is published to secure prior art and support further research in self-validating AI systems, semantic stability, and thermodynamic computing.