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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).

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