Thermodynamic modifications to Bardeen black holes surrounded by quintessence based on the new higher order GUP

In this article, the thermodynamic properties of Bardeen black holes surrounded by quintessence are investigated in the framework of a new higher order GUP. The modified Hawking temperature, entropy and heat capacity are derived using a heuristic approach. Meanwhile, the remnant temperature and mass are deduced, and the modified black hole state equation is obtained by utilizing the energy density of matter. Ultimately, we analyze the effects of the GUP controlling deformation parameter $\beta$ on these thermodynamic properties using graphical illustrations, to more comprehensively understand the thermodynamic behavior of the black hole in the context of higher order GUP.