Holographic Renyi Entropy at High Energy Density

Abstract

We show that Renyi 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 Renyi entropies in a particular thermodynamic limit with high energy density and fixed fractional size of the subregion. Holographically, the Renyi 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.

6 pages, 2 figures; v2: title slightly changed, new references and minor clarifications added, version to be published in PRL