Lindblad dynamics in holography

We develop, in the AdS/CFT correspondence, a method to compute correlation functions when the CFT is governed by the Lindblad equation for open quantum systems, via the AdS theory. Using a simple example in AdS${}_3$/CFT${}_2$, we demonstrate that the predictions of the AdS theory based on our method match the direct computations in the dual CFT. We also briefly discuss the relaxation problem and the holographic entropy in this example.