AdS黑洞的热力学曲率及其相变动力学研究

黑洞热力学的发展为研究引力的量子化提供了新视角，尤其是AdS黑洞中扩展相空间的引入，衍生出了丰富的的热力学相变现象。目前对黑洞相变的研究大多是关于相变类型和临界性的分析，而对相变的微观机制和动力学行为还不清楚。本项目拟探索AdS黑洞发生相变时的物理过程，阐释黑洞热力学相变为何发生以及怎样发生的问题。一方面，热力学几何理论现在可以认为是从热力学角度探索系统微观信息的一个潜在手段，在黑洞热力学微观行为的分析中起着重要作用；另一方面，相变的发生涉及非平衡统计理论，就需要利用相关随机过程内容对相变进行动态分析。项目着眼于探索热力学曲率与黑洞热力学微观结构之间的关联性以及寻找动态描述黑洞相变的合适序参量和特性函数，以获取黑洞相变的微观机制和动力学相关信息。该项目的实施，将加深对黑洞宏观热力学量在其微观行为以及相变中作用的深层次理解和认识，对建立黑洞的统计力学具有启示意义。

The development of black hole thermodynamics provides a new perspective for the study of the quantization of gravity. Especially, the introduction of extended phase space in AdS black holes leads to abundant thermodynamic phase transition phenomena. At present, the research on black hole phase transition is mostly about the type of phase transition and criticality , while the micro-mechanism and dynamics of phase transition are still unclear. This project plans to explore the physical process of the phase transition of AdS black holes, and explain why and how the black hole thermodynamic phase transition occurs. On the one hand, the thermodynamic geometry theory can now be considered as a potential means to explore the microscopic information of the system from the perspective of thermodynamics, which plays an important role in the analysis of the thermodynamic microscopic behavior of black holes. On the other hand, the occurrence of the phase transition involves non-equilibrium statistical theory, so it is necessary to use the relevant stochastic process to conduct dynamic analysis of the phase transition. The project focuses on exploring the correlation between the thermodynamic curvature and the thermodynamic micro-structure of black holes, as well as finding the appropriate order parameters and characteristic functions to dynamically describe the phase transition of black holes, so as to obtain the micro-mechanism and dynamic information of the black hole phase transition. The implementation of this project will deepen the deep understanding of the role of black hole macro-thermodynamics in its micro-behavior and phase transition, and have enlightenment significance for the establishment of black hole statistical mechanics.