  Treating the horizon radius as an order parameter in a thermal fluctuation,
the free energy landscape model sheds light on the dynamic behaviour of black
hole phase transitions. Here we carry out the first investigation of the
dynamics of the recently discovered multicriticality in black holes. We
specifically consider black hole quadruple points in D=4 Einstein gravity
coupled to non-linear electrodynamics. We observe thermodynamic phase
transitions between the four stable phases at a quadruple point as well as the
weak and strong oscillatory phenomena by numerically solving the Smoluchowski
equation describing the evolution of the probability distribution function. We
analyze the dynamic evolution of the different phases at various ensemble
temperatures and find that the probability distribution of a final stationary
state is closely tied to the structure of its off-shell Gibbs free energy.
