Thermodynamic properties and Joule-Thomson expansion of AdS black hole with Gaussian distribution in non-commutative geometry

The thermodynamics and Joule-Thomson expansion of anti-de Sitter black hole (AdS BH) with Gaussian distribution in non-commutative geometry is systematically studied. The metric of Gaussian-distributed BH is obtained, showing a dS geometry at the core of BH. The research indicates that the BH characterized by a Gaussian distribution exhibit thermodynamic properties that are remarkably similar to those of BH with a Lorentzian distribution in non-commutative geometry. This similarity is specifically manifested in the small BH-large BH phase transition, the corrected first law of thermodynamics, the criticality, the heat capacity, the zeroth-order phase transition and the Joule-Thomson process. Notably, the critical ratio of Gaussian-distributed BH (0.46531) is significantly larger than those observed in Van der Waals fluids (0.375), and indeed, it is also substantially exceed those of Lorentzian-distributed BH (0.36671). Moreover, compared to the case of Lorentzian source, the zeroth-order phase transition effect in Gaussian-distributed BH is exceedingly subtle (accompanied by a relative increase in the Gibbs free energy on the order of $10^{-3}\!\sim\!\!10^{-2}$) and is difficult to detect distinctly.