Thermodynamic of a rotating and Non-linear magnetic-charged black hole in the quintessence field

Abstract: We purpose an approach for the thermodynamic analysis of rotating and non-linear magnetic-charged black hole with quintessence. Accordingly, we compute various thermodynamics quantities of the black hole, such as mass, temperature, potential provided from the magnetic charge, and the heat capacity. Moreover, we study phase transitions of this black hole, analyzing the plot of its heat capacity. Then, we have shown that the black hole mass would have a phase of decrease, while the temperature increases from negative absolute temperatures. From the behavior of the heat capacity, we point out that the black hole undergoes to a second-order phase transition, which is shifted towards the higher values of entropy as we increase the rotating parameter $a$ or the magnetic parameter $Q$.