  We propose a new approach to study the dynamical phase transition of RNAdS
black holes on the underlying free energy landscape. By formulating a path
integral framework, we can quantify the kinetic paths representing the history
from the initial state to the end state, which provides us a visualized yet
quantified picture about how the phase transition proceeds. Based on these
paths, we derive the analytical formulas for the time evolution of the
transition probability and provide a physical interpretation of the
contribution to the probability from one "pseudomolecule"
("anti-pseudomolecule"), which is actually the phase transition rate from the
small(large) to the large(small) black hole state. These numerical results show
a good consistency with the underlying free energy landscape topography.
