Quantum coherence is increasingly recognised as a thermodynamic resource that free energy alone cannot describe. This work develops a phenomenological thermodynamics for coherence-information (C-I) systems, idealised systems composed only of information and the coherent relations among its elements, and tests a numerical realisation of it against black-hole morphology. A minimum-action postulate, $\Delta C\cdot\Delta I \geq h/\pi$, is combined with a gradient-based semantic entropy and an equipartition-based semantic temperature to formulate five laws and three dimensionally consistent operating modes. For black holes the framework gives a thermodynamic coherence $C_T = 2/(Mc^2)$, which grow... More >