How can we detect the difference in the effects of the quantum corrections included in the metric of a spacetime and the quantum corrections included in the entropy of such a system? Recently, J. Barrow designed an expression based directly on black hole (BH) entropy of Bekenstein-Hawking where the geometry of the event horizon can also have an intricate, non smooth, structure, a fractal geometry. These fractal features are represented by a numerical constant parameter, the fractal parameter (FP). Since then, several interesting issues have been explored in the literature. In this work, we investigate the inversion temperature connected to the Joule-Thomson expansion from the thermodynamics of AdS-Reissner-Nördstrom BH by using the Barrow entropy equation where the FP has several values within a certain validity interval. We include quantum corrections in a cosmological fluid that can describe phantom dark matter or quintessence, both in a Kiselev scenario. The description of such physical systems also involves numerical solutions concerning the FP. The results are shown by temperature-pressure curves for multiple values of the parameters of the system used here. In conclusion of our analysis, we also show isenthalpic curves corresponding to fixed-mass BH processes, and we respond numerically to the question made in the first line of this abstract.
Abreu et al. (Wed,) studied this question.