  We consider a central system which is coupled via dephasing to an open
system, i.e. an intermediate system which in turn is coupled to another
environment. Considering intermediate and far environment as one composite
system, the coherences in the central system are given in the form of fidelity
amplitudes for a certain perturbed echo dynamics in the composite environment.
On the basis of the Born-Markov approximation, we derive a master equation for
the reduction of that dynamics to the intermediate system alone. In distinction
to an earlier paper [arXiv: 1502.04143 (2015)] where we discussed the
stabilizing effect of the far environment on the decoherence in the central
system, we focus here on the possibility to use the measurable coherences in
the central system for probing the open quantum dynamics in the intermediate
system. We illustrate our results for the case of chaotic dynamics in the near
environment, where we compare random matrix simulations with our analytical
result.
