Revisiting the Born-Infeld-AdS black hole phase structure through Landau theory and free energy landscape approaches.

In our present work, we probe the thermal phase transition structure, the dynamic and kinetic behavior of the Born-Infeld-AdS black hole. With the emergence of a triple point behavior and the possible ruling out the reentrant phase transition, for a certain parametric value of the charge parameter, we scrutinize the stochastic dynamics and the kinetic processes using the free energy landscape formalism. Such processes occur during the black hole phase transitions in terms of the Landau functional and equivalently by the Fokker-Planck equation in the context of black hole chemistry. Our analysis establishes a pertinent bridge between the thermal behavior among the different states of the Van-der-Waals-like fluids and the Born-Infeld-AdS black hole phases. To visualize the direct implications of the Landau functional of the usual Van-der-Waals-like fluids, we consistently employed the generic Landau formalism. We find that such investigations are worthy of study in implementing the continuous phase transition behavior during Hawking radiation. For more details, and in addition to the exploitation of the Landau functional, we introduce its convexity to determine its extreme points and the corresponding stable and unstable phases of the thermal black hole systems. We systematically study the behavior of the first-order and the second-order phase transitions and look into details of their evolution during thermal transitions. Moreover, knowing that the thermal phase transitions are controlled through a stochastic process depending upon an order parameter, the dynamics during its phases are determined through the fluctuating macroscopic variables, we recall the dynamical Fokker-Planck equation to furnish the advancement of such a process in the Born-Infeld-AdS background with a special focus on the probability distribution of the triple point. The evolution of the initial probability indicates that not only the initial small black hole to the final large black hole phase occurs, but also one has the equilibrium conditions established among the thermal radiations to the small black holes or the large black holes to thermal radiations and large black hole states. We also demonstrate the first passage time for the different black hole phase behaviors to determine their time scale using the Crank-Niclson method. Such a study has implications for the friction effects of the kinetic turnover of different black hole phases and consequently a direct connection to the microscopic degrees of freedom.