Coherence Thermodynamics: A Framework for Semantic Systems

Classical thermodynamics describes energy and entropy in physical systems but lacks a framework for information-processing systems where meaning, coherence, and contradiction resolution play fundamental roles. We develop Coherence Thermodynamics, a rigorous extension of thermodynamic principles to semantic systems, by redefining temperature as semantic agitation energy, entropy as semantic disorder intensity, and heat as contradiction transfer across coherence boundaries. We establish four fundamental laws: a zeroth law defining semantic thermal equilibrium through temperature equality, a first law incorporating coherence work terms into energy conservation, a second law permitting local entropy reduction via contradiction metabolism while preserving global entropy increase, and a fourth law governing semantic force dynamics via a generalized Navier-Stokes equation driven by coherence gradients and information-theoretic inertia. All formulations maintain strict dimensional consistency and provide operational definitions through measurable field quantities defined on classical spacetime. Coherence Thermodynamics offers a mathematically rigorous foundation for the quantitative analysis of information processing, artificial intelligence, and biological cognition, establishing thermodynamic principles as universal laws governing both physical energy and semantic meaning across all scales of organization.