扩展相空间黑洞相变的微观、统计诠释以及全息热机的研究

Considering the variation of the cosmological constant and identifying the cosmological constant as thermodynamic pressure of black holes, the extended phase space thermodynamics especially black hole phase transition has become the international research frontier. Exploring the theoretical mechanism of black hole phase transition in the extended phase space, especially from the microscopic and statistical mechanical perspective, is both of great scientific importance and very challenging. This project is both the further probe in theory and extension in application of our work in the past few years. It consists of the following aspects. (1) Probe the influence of dark energy and modified gravity theories on the efficiency of holographic heat engine and the mechanism; (2)Utilize the thermodynamic geometry to explain from the microscopic perspective why some AdS black holes do not exhibit Van der Waals like P-V criticality; (3) From the perspective proposed by Dvali and Gomoz that black hole can be viewed as Bose-Einstein condensation of gravitons, disclose the mechanism of black hole phase transition in the extended phase space in the statistical level. The latter is a totally new approach, thus is the most challenging aspect in this project. This project will deepen the understanding of holographic heat engine and black hole phase transition in the microscopic and statistical level. On the other hand, it will also help understand dark energy and modify gravity theories.

考虑宇宙学常数的变化，并将宇宙学常数对应为黑洞的热力学压强，扩展相空间黑洞热力学尤其是黑洞相变近几年已经成为国际研究前沿。深入挖掘扩展相空间黑洞相变理论机制，尤其从微观和统计的层面揭示其规律，具有重要的科学意义同时也具有很大的挑战性。本项目是申请人过去几年工作在理论上的深入以及应用上的拓展。研究内容包括：（1）探索暗能量和修正引力理论对全息热机效率的影响及影响机制；（2）利用热力学几何工具从微观上诠释扩展相空间有些AdS黑洞为何不存在类范德瓦耳斯气体的P-V临界现象；（3）结合Dvali和Gomoz提出的黑洞可以理解为引力子的玻色—爱因斯坦凝聚的视角，尝试从统计层面揭示扩展相空间黑洞相变的机理。后者是一项全新的课题，因而也是本项目最具挑战性的内容。本项目的研究一方面促进人们对全息热机以及在微观和统计层面对扩展相空间黑洞相变更深刻的理解，另一方面也将促进对暗能量和修正引力理论的理解。

考虑宇宙学常数的变化，并将宇宙学常数对应为黑洞的热力学压强，扩展相空间黑洞热力学尤其是黑洞相变已经成为国际研究前沿。深入挖掘扩展相空间黑洞相变理论机制，具有重要的科学意义同时也具有很大的挑战性。本项目紧密围绕原计划中的“扩展相空间黑洞相变”以及“全息热机”两大研究领域展开。取得的研究进展如下（1）通过一系列的工作，分别揭示了massive引力、时空维度、phantom暗能量对黑洞全息热机效率的影响。（2）通过一系列的工作，从多个维度深入探索了扩展相空间黑洞相变的性质及机制。譬如通过热力学几何等有效工具研究一些较为复杂的黑洞相变，揭示了多种物理因素对扩展相空间黑洞相变的协同作用；通过一些独特的视角重新认识了扩展相空间黑洞相变，例如纠缠熵、两点关联函数等局域观测量视角以及将Lovelock参量看作变量的新视角；通过对临界点物理量比值普适性的探求，更深刻地理解扩展相空间黑洞相变的性质。另外，本项目还分别揭示了Lovelock引力以及时空维度对黑洞焦耳-汤姆逊膨胀的作用。