Coherence Thermodynamics: A Phenomenological Framework and a Numerical Field Model for Black-Hole Morphology

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 grows as the hole loses mass. A three-dimensional field model encodes U(1), $\mathbb{Z}_2$ and $\mathbb{Z}_3$ symmetry breaking through the geometric phase $m\theta + \omega R + \lambda_{\mathrm{vert}}\cos\phi$ and was examined with grid-convergence tests, control runs with azimuthal orders $m = 1$-$6$ and closed-form predictions. The azimuthal phase contains a phase-defect line on the symmetry axis. Without regularisation, the maximum field gradient scales inversely with the grid spacing and the axial enhancement of the certainty ratio grows with resolution. With a core radius $a \geq 0.5$, all diagnostics converge to within 3%. The number of decoherence maxima is always $2m$, so the six hot-spot-like features follow directly from the choice $m = 3$. Their spiral pitch, $-\omega/m$, and hemispheric twist, $-2\lambda_{\mathrm{vert}}\cos\phi/m$, agree with the simulations to within 9% and 0.3%, respectively. The model therefore maps imposed symmetry parameters onto observable morphology through explicit relations, yielding falsifiable predictions such as a flux quasi-periodicity at $2m$ times the hot-spot orbital frequency, while its astrophysical interpretation remains phenomenological.