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.

我们的目的是对具有精髓的旋转非线性带磁黑洞进行热力学分析。因此，我们计算了黑洞的各种热力学量，例如质量、温度、磁荷提供的电势和热容。这使我们能够欣赏精髓如何改变黑洞的行为。此外，我们研究了这个黑洞的二阶相变，分析了它的热容量图。然后，我们表明黑洞质量将有一个减少的阶段。从热容的行为中，我们指出黑洞经历了二阶相变，随着我们增加旋转参数a或磁参数Q，它向更高的熵值移动. 然而，我们发现当我们增加典型参数c 时，二阶相变反而转移到较低的熵值。