Classical thermodynamics describes energy and entropy in physical systems, but lacks a framework for understanding 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 defining temperature as semantic agitation energy, entropy as semantic disorder intensity, and heat as contradiction transfer across coherence boundaries. We establish five fundamental laws: a zeroth law defining semantic thermal equilibrium through temperature equality, a first law incorporating coherence work terms, a second law allowing local entropy decrease through contradiction metabolism while preserving global entropy increase, a third law describing semantic superconductivity at absolute zero, and a Navier-Stokes equation governing semantic force density evolution. All formulations maintain strict dimensional consistency and provide operational definitions through measurable field quantities defined on classical spacetime. The framework predicts testable phenomena including semantic lensing effects in AI training dynamics, coherence dependent processing efficiency in neural systems, and contradiction driven phase transitions in meaning-processing systems. Coherence Thermodynamics provides a mathematically rigorous foundation for quantitative analysis of information processing, artificial intelligence dynamics, and biological cognition, establishing thermodynamic principles as universal laws governing both physical energy and semantic meaning across all scales of organization.