Holographic Renyi Entropy at High Energy Density. (arXiv:1811.04081v2 [hep-th] UPDATED)
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.