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We propose that the thermodynamics and the kinetics of the phase transitionbetween wormhole and two black hole described by the two coupled SYK model canbe investigated in terms of the stochastic dynamics on the underlying freeenergy landscape. We assume that the phase transition is a stochastic processunder the thermal fluctuations. By quantifying the underlying free energylandscape, we study the phase diagram, the kinetic time and its fluctuations indetails, which reveal the underlying thermodynamics and kinetics. It is shownthat the first order phase transition between wormhole and two black holedescribed by two coupled SYK model is analogous to the Van der Waals phasetransition. Therefore, the emergence of wormhole and two black hole phases, thephase transition and associated kinetics can be quantitatively addressed in ourfree energy landscape and kinetic framework through the dependence on thebarrier height and the temperature.

Free energy landscape and kinetics of phase transition in two coupled SYK models