Department of Physics, University of California, Santa Barbara, California 93106, USA.
Phys Rev Lett. 2019 Feb 1;122(4):041602. doi: 10.1103/PhysRevLett.122.041602.
We show that Rényi entropies of subregions can be used to distinguish when the entire system is in a microcanonical ensemble from when it is in a canonical ensemble, at least in theories holographically dual to gravity. Simple expressions are provided for these Rényi entropies in a particular thermodynamic limit with high energy density and fixed fractional size of the subregion. Holographically, the Rényi entropies are determined by the areas of cosmic branes inserted into the bulk spacetime. They differ between a microcanonical and a canonical ensemble because the two ensembles provide different boundary conditions for the gravitational theory under which cosmic branes lead to different backreacted geometries. This is in contrast to the von Neumann entropy which is more coarse-grained and does not differentiate microcanonical ensembles from canonical ensembles.
我们表明，子区域的 Renyi 熵可用于区分整个系统处于微正则系综还是正则系综，至少在与引力全息对偶的理论中是这样。我们提供了这些 Renyi 熵在具有高能量密度和固定子区域分数大小的特殊热力学极限下的简单表达式。从全息的角度来看，Renyi 熵由插入到 bulk 时空中的宇宙膜的面积决定。它们在微正则系综和正则系综之间有所不同，因为这两个系综为宇宙膜导致不同的反作用几何形状的引力理论提供了不同的边界条件。这与 von Neumann 熵形成对比，后者更粗糙，不能区分微正则系综和正则系综。
