Thermodynamics of a rotating and non-linear magnetic-charged black hole in the quintessence field

We purpose an approach for the thermodynamic analysis of a rotating and non-linear magnetic-charged black hole with quintessence. Accordingly, we compute various thermodynamic quantities of the black hole, such as mass, temperature, potential provided from the magnetic charge, and the heat capacity. This allows us to appreciate how quintessence modifies the behaviour of the black hole. Moreover, we study second-order phase transitions of this black hole, analysing the plot of its heat capacity. Then, we show that the black hole mass would have a phase of decrease. From the behaviour of the heat capacity, we point out that the black hole undergoes to a second-order phase transition, which is shifted towards higher values of entropy as we increase the rotating parameter a or the magnetic parameter Q. However, we have found that when we increase the quintessence parameter c, the second-order phase transition is instead shifted to lower entropy values.