  We start with a brief overview of the basic thermodynamic properties of the
Born-Infeld metric in AdS spacetime. Using the concept of the enthalpy
characterizing the total mass of the black hole, in our present paper, we probe
the thermal phase transition structure, the dynamic and kinetic behavior of the
Born-Infeld-AdS black hole. The emergence of the triple point behavior and the
possible ruling out the reentrant phase transition, for a certain parametric
value of the charge on the free energy landscape, we scrutinize the stochastic
dynamics and the kinetic processes. We describe such processes 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 holes 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 for the analysis of the black hole phase
transitions of the Born-Infeld-AdS black holes. We find that such
investigations are worthy of study in implementing the continuous phase
transition behavior during the Hawking radiation. For more details, and in
addition to the exploitation of the Landau functional, we introduce ...
