  We investigate the possibility to monitor the dynamics of an open quantum
system with the help of a small probe system, coupled via dephasing coupling to
the open system of interest. As an example, we consider a dissipative harmonic
oscillator and a single qubit as probe system. Qubit plus oscillator are
described by a finite temperature quantum master equation, where the dynamics
of the whole system can be obtained analytically. We find that the short time
behavior of the reduced qubit state (its coherence) provides exhaustive
information on the dissipative dynamics of the oscillator. Observing this
coherence for two initial states with different out-of-equilibrium
temperatures, one can determine all coupling constants and the equilibrium
temperature fixed by the external heat bath. In addition, the dephasing
coupling to the qubit probe, may be considered as a perturbation of the
dissipative oscillator. The corresponding quantum fidelity can be calculated
analytically, also. Hence, we find the precise relation between the behavior of
the reduced qubit state (its coherence) and that fidelity.
