Ali Md Sabir, El Moumni Hasan, Khalloufi Jamal, Masmar Karima
Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246, India.
LPTHE, Physics Department, Faculty of Sciences, Ibnou Zohr University, B.P 8106, Agadir, Morocco.
Sci Rep. 2025 May 2;15(1):15425. doi: 10.1038/s41598-025-88842-3.
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.
在我们目前的工作中，我们探究了玻恩-因费尔德-反德西特（Born-Infeld-AdS）黑洞的热相变结构、动力学和动理学行为。随着出现的三相点行为以及可能排除再入相变，对于电荷参数的特定参数值，我们使用自由能景观形式来仔细研究随机动力学和动理学过程。在黑洞化学的背景下，此类过程在黑洞相变期间根据朗道泛函并等效地通过福克-普朗克方程发生。我们的分析在类范德瓦尔斯流体不同状态间的热行为与玻恩-因费尔德- AdS黑洞相之间建立了一座相关的桥梁。为了直观呈现通常类范德瓦尔斯流体朗道泛函的直接影响，我们始终采用通用的朗道形式。我们发现此类研究对于在霍金辐射期间实现连续相变行为而言值得探讨。更详细地说，除了利用朗道泛函之外，我们引入其凸性来确定其极值点以及热黑洞系统相应的稳定和不稳定相。我们系统地研究一阶和二阶相变的行为，并深入研究它们在热转变期间的演化细节。此外，鉴于热相变是通过依赖于序参量的随机过程来控制的，其相变期间的动力学是通过波动的宏观变量来确定的，我们回顾动力学福克-普朗克方程，以阐述在玻恩-因费尔德- AdS背景下此类过程的进展，特别关注三相点的概率分布。初始概率的演化表明，不仅发生了从初始小黑洞到最终大黑洞相的转变，而且在热辐射到小黑洞或大黑洞到热辐射以及大黑洞状态之间建立了平衡条件。我们还使用克兰克-尼科尔森（Crank-Niclson）方法展示了不同黑洞相行为的首次通过时间，以确定它们的时间尺度。此类研究对于不同黑洞相的动理学周转的摩擦效应具有启示意义，从而与微观自由度有直接联系。
