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The perturbation correction of general relativity has obtained the generalrelationship between entropy and extremality. The relation was found to exactlyhold for the charged AdS black hole, and extended to the rotating and massivegravity black holes. In this paper, We confirm the universal relation for thefour dimensional RN-AdS black hole surrounded by the quintessence, and find anew extremality relation between black hole mass and the normalization factor$a$ related to the density of quintessence. Besides, we also find that when theblack hole entropy increases, the correction constant is negative, the blackhole mass and the mass-charge ratio decreases, hence this black hole displaysWGC-like behavior. Moreover, we derive the general relationship on nonlinearelectrodynamic source couples to AdS spacetime with quintessence field. We findanother new extremality relation between black hole mass and the magneticmonopole charge $\beta$.

Universal thermodynamic extremality relations for charged AdS black hole surrounded by quintessence