Employing the free energy landscape, we study the phase transition and its dynamics for a class of regular black holes in Anti-de Sitter spacetime governed by the coupling of non-linear electrodynamics, which reduces to Hayward and Bardeen solutions for particular values of spacetime parameters. The Fokker-Planck equation is solved numerically by imposing the reflecting boundary condition and a suitable initial condition, using which, we investigate the probabilistic evolution of regular AdS black holes. In this approach, the on-shell Gibbs free energy is treated as a function of the radius of the event horizon, which happens to be the order parameter of the phase transition.The numerical solution is also obtained for the absorbing boundary condition. The dynamics of switching between the coexistence small black hole phase and large black hole phase due to the thermal fluctuation is probed by calculating the first passage time. The effect of temperature on the dynamical process is also investigated.

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In this article, we analytically investigate the microstructure of a five-dimensional neutral Gauss-Bonnet black hole, in the background of anti-de Sitter spacetime, using scalar curvature of the Ruppeiner geometry constructed via adiabatic compressibility. The microstructure details associated with the small-large black hole phase transition are probed in the parameter space of pressure and volume. The curvature scalar shows similar properties for both phases of the black hole, it diverges in the vicinity of critical point and approaches zero for extremal black holes. We show that the dominant interaction among black hole molecules is attractive. This study also affirms that the nature of the microstructure interaction remains unchanged during the small-large black hole phase transition, even though the microstructures are different for both phases.

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