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We start with a brief overview of the basic thermodynamic properties of theBorn-Infeld metric in AdS spacetime. Using the concept of the enthalpycharacterizing the total mass of the black hole, in our present paper, we probethe thermal phase transition structure, the dynamic and kinetic behavior of theBorn-Infeld-AdS black hole. The emergence of the triple point behavior and thepossible ruling out the reentrant phase transition, for a certain parametricvalue of the charge on the free energy landscape, we scrutinize the stochasticdynamics and the kinetic processes. We describe such processes during the blackhole phase transitions in terms of the Landau functional and equivalently bythe Fokker-Planck equation in the context of black hole chemistry.  Our analysis establishes a pertinent bridge between the thermal behavioramong the different states of the Van-der-Waals-like fluids and theBorn-Infeld-AdS black holes phases. To visualize the direct implications of theLandau functional of the usual Van-der-Waals-like fluids, we consistentlyemployed the generic Landau formalism for the analysis of the black hole phasetransitions of the Born-Infeld-AdS black holes. We find that suchinvestigations are worthy of study in implementing the continuous phasetransition behavior during the Hawking radiation. For more details, and inaddition to the exploitation of the Landau functional, we introduce ...

Born-Infeld-AdS black hole phase structure: Landau theory and free energy landscape approaches