In the perturbative treatment of, let's say, a scalar field theory on AdS spacetime, the correlation functions decay exponentially at late times, indicating, as people say, information loss.
I guess there are two questions I'd like a clarification for:
1) How can I see that the exponential decay of correlations and information loss are related? Is there a mathematical treatment that links both notions together?
2) Is decay of correlation functions at late time ALWAYS indicating information loss, even if it is power-law like, or even slower than that?
Other than an informed answer, I would appreciate some references for further reading, that help connect the two notions together (they could be from different fields in Physics for example).