Numerical Implementation of Coherence Thermodynamics: Computational Framework for Semantic Field Dynamics

Classical thermodynamics lacks a framework for analyzing systems whose primary function is semantic processing and meaning-making. We present the first computational implementation of Coherence Thermodynamics, a theoretical extension of thermodynamic principles to semantic systems that treats coherence as a fundamental quantity analogous to energy. The framework operationalizes semantic temperature through contradiction gradient magnitude, semantic entropy via local coherence decay, and quantum processing limits through the action bound relating coherence fluctuation and semantic impulse. Using spatially extended field representations on a discrete grid, we simulate the thermodynamic behavior of semantic contradiction processing and coherence maintenance. The computational results reveal organized spatial structures rather than uniform distributions: semantic entropy localizes in high-gradient regions, semantic free energy exhibits bilateral minima functioning as thermodynamic attractors, and heat flux follows classical Fourier transport with directed flow from high to low semantic temperature zones. The collapse functional and certainty ratio provide operational measures for tracking proximity to quantum threshold violations, with spatial correlation between elevated certainty values and contradiction intensity confirming recursive dynamics. Under the tested parameter regime, the system operates in a sub-threshold regime with structured thermodynamic organization. The computational framework demonstrates formal mathematical parallels to black hole thermodynamics and cosmological structure formation, suggesting potential universality in constraint-driven entropy maximization across physical and informational systems. This work establishes numerical foundations for analyzing semantic processing through thermodynamic principles, enabling quantitative investigation of meaning-making as a thermodynamic process governed by measurable field variables and fundamental physical constraints.