；.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。

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.