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).

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).