引力热力学和引力流体对偶

The black-hole thermodynamics has inspired some profound ideas about the spacetime and gravity, such as the holographic principle and the emergence of gravity. This project will explore the correspondence between gravity and thermodynamics as well as gravity and hydrodynamics. We will study the spacetime thermodynamics of the diffeomorphism-invariant modified gravity, such as Lovelock gravity, f(R) gravity, and scalar-tensor gravity, focusing on the nonequilibrium entropy production and the dissipation of horizon perturbations that will be compared with the viscosity coefficients calculated from membrane paradigm and gauge/gravity correspondence. This could shed light on the underlying microcosmic degree of freedom of spacetime. In terms of the gravitational field equation or the Friedmann equation, we will investigate the first law of thermodynamics, Smarr formula, holographic entropy bound, and Cardy-Verlinde formula on the holographic screen, all of which will benefit to realize what is the real residence of the spacetime thermodynamics, and increase the understanding on the temperature of spacetime, gravitational entropy, and quasilocal gravitational energy. Moreover, we will study how to extract the Navier-Shokes equation in the finite cut-off surface from the modified gravity, and will describe the hydrodynamics by the extremization principle of entropy，similar to the analogy between the spacetime and solid. We ultimately expect to find the new hint of quantum spacetime.

；.黑洞热力学已经启发了一些关于时空和引力本质的深刻观点,例如全息原理和引力的呈展性。本项目将探索引力和热力学以及引力和流体力学的对应关系。我们将研究微分同胚不变的修正引力理论,如LoveLock,f(R)和标量张量引力的时空热力学,着重关注非平衡熵增和视界扰动的耗散效应,并和用膜范式以及规范/引力对偶计算得到的流体的粘滞系数比较, 以此作为了解时空微观自由度的窗口。我们将用引力场方程或者Friedmann方程研究全息屏上热力学第一定律、Smarr公式、全息熵界和Cardy-Verlinde公式,以期认识时空热力学体系的真正依附,并增进对时空温度、引力熵、准局域引力能量的理解。我们还将研究有限截断面上如何从修正引力理论得到Navier-Stokes方程,并按照时空固体类比方法，从熵极值原理得到流体力学的热力学描述。我们最终希望找到时空量子理论的新线索。

黑洞热力学启发了一些关于引力和时空本质的深刻观点，例如全息原理和引力的呈展性。本项目利用热力学、流体力学和全息对偶的方法研究引力的性质和引力理论在凝聚态物理中的应用。我们首先研究标量-张量引力中存在的自发诱导的广义相对论。我们证明具有宇宙常数和任意截面曲率的外部施瓦希时空可与一个新奇的内核相连接，该内核具有冻结光线和局域的全息熵填充等有趣的性质。其次，我们研究了强耦合场论在整体淬火后的热化过程。通过纠缠熵和交互信息这两个非局域可观测量，我们找到全息热化的一些普遍性质。再次，我们研究了分数量子霍尔流体具有的时空对称性，发展了基于Newton-Cartan几何的非相对论场论的协变描述，并以此为基础构建了分数量子效应的全息模型，第一次在非相对论全息理论中实现了霍尔粘滞和轨道角动量密度的关系。此外，我们推导了处在背景场中的协变的黑洞热力学第一定律，我们发现黑洞熵依附视界的局域性是识别黑洞熵协变表示的关键，而微分同胚对称不再是构建黑洞熵的充分必要条件。最后，我们利用全息截断面上的热电输运研究了量子临界金属。我们发现一种复合扩散模式在高温下具有普遍性，这可能有助于理解奇异金属中普遍存在的线性电阻现象。