The decay of the left-right correlators in an eternal black hole is one of the simplest manifestations of the black hole information loss problem.
The subalgebras of left and right decorrelate under the time evolution asymptotically, and monotonically due to the stretching of the wormhole.
From the point of view of quantum mechanics, dynamical decorrelation is so special that can be used as a clue to the nature of operator algebras in quantum gravity.
In particular, I will argue that asymptotic decorrelation uniquely fixes the operator algebras to be the type III1 von Neumann algebras. I will comment on the connections between the emergence of the second law, the decay of the out-of-time-ordered correlator (chaos), and the emergence of type III1 algebras.