Exploring the gauge/gravity duality of a generalized von Neumann entropy
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We consider a generalized von Neumann entropy that depends only on the density matrix. This is based on a modification of Boltzmann-Gibbs entropy by considering non-equilibrium systems on stationary states, and an entropy functional depending only on the probability. We propose a generalization of the replica trick and find that the resulting modified von Neumann entropy is precisely the previously mentioned entropy that was obtained by other assumptions. Then, we address the question whether alternative entanglement entropies can play a role in the gauge/gravity duality. Our focus are 2d CFT and their gravity duals. Our results show corrections to the von Neumann entropy S0. If the central charge is small/large they are correspondingly larger/smaller than the usual UV ones and also than the corrections to the corresponding minimal length in AdS3, which are comparable to the UV ones. This agrees with previous results indicating that the generalized entropy is more relevant for systems with fewer degrees of freedom. The correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT and the gravitational AdS3 minimal length. We discuss the ingredients for computing the corresponding gravity duals of generalized entanglement entropies.
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