  We propose that the thermodynamics and the kinetics of the phase transition
between wormhole and two black hole described by the two coupled SYK model can
be investigated in terms of the stochastic dynamics on the underlying free
energy landscape. We assume that the phase transition is a stochastic process
under the thermal fluctuations. By quantifying the underlying free energy
landscape, we study the phase diagram, the kinetic time and its fluctuations in
details, which reveal the underlying thermodynamics and kinetics. It is shown
that the first order phase transition between wormhole and two black hole
described by two coupled SYK model is analogous to the Van der Waals phase
transition. Therefore, the emergence of wormhole and two black hole phases, the
phase transition and associated kinetics can be quantitatively addressed in our
free energy landscape and kinetic framework through the dependence on the
barrier height and the temperature.
