Effects of dark energy on dynamic phase transition of charged AdS black holes

In a search for the effects of quintessence dark energy on the kinetics of black hole phase transition, we investigate in detail the dynamic phase transition of charged anti-de Sitter black holes surrounded by quintessence in this paper. We compare the case with dark energy and the case without dark energy. It is shown that the initial black hole state evolves more quickly in the case with dark energy than in the case without dark energy, no matter what the initial black hole state is. The result concerning the first passage process further supports this finding. The transition from the large (small) black hole state to the small (large) black hole state happens quickly. Last but not least, we calculate the mean first passage time for various choices of parameter coq. It is shown that the mean first passage time for the case with dark energy is much shorter than that of the case without dark energy, which can be understood by the result that the height of the barrier of Gibbs free energy for the case with dark energy is lower than that of the case without dark energy. Interestingly enough, the effect of dark energy is quite unique. For the range of coq, there exists a minimum mean first passage time. With the increasing of coq from -0.99 to -0.34, the mean first passage time decreases dramatically and then increases. Considering the mean first passage time is an observable of black hole dynamic phase transition, the unique results we obtain here may shed new light on constraining the parameters of the quintessence dark energy theory based on future observations.