Thermodynamics of the Reissner-Nordström black hole with quintessence matter on the EGUP framework

Abstract: In this paper, we investigate the quantum correction on thermodynamics of the Reissner-Nordstr\"om black hole in the presence of the quintessence matter associated with dark energy. To this end, the modified Hawking temperature, heat capacity, and entropy functions of the black hole are derived. { Investigation reveals that the modified uncertainty principles and normalization factor $\alpha$ restrict the lower bound value of horizon radius to affect the Hawking temperature and the parameter $\eta_{0}$ have a non-negligible effect on the heat capacity threshold.} {Furthermore}, the correction of entropy does not depend on the quintessence matter. It is also examined the equation of state associated with the pressure and the volume in this framework. In addition, we employ graphical methods to compare and discuss the findings within the generalized uncertainty principle (GUP) and extended uncertainty principle (EUP).