  We consider discrete quantum systems coupled to finite environments which may
possibly consist of only one particle in contrast to the standard baths which
usually consist of continua of oscillators, spins, etc. We find that such
finite environments may, nevertheless, act as thermostats, i.e., equilibrate
the system though not necessarily in the way predicted by standard open system
techniques. Thus, we apply a novel technique called the Hilbert space Average
Method (HAM) and verify its results numerically.
