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 Γ(χ ²) distribution that depends on β 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. (paper)