Generalized Entanglement Entropy and Holography

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Gamma(chi(2)) distribution that depends on beta and also on p(l). The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2dCFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV (for c = 1) ones and also than those due to the area dependent AdS(3) entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS(3) area dependent entropy.