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We consider discrete quantum systems coupled to finite environments which maypossibly consist of only one particle in contrast to the standard baths whichusually consist of continua of oscillators, spins, etc. We find that suchfinite environments may, nevertheless, act as thermostats, i.e., equilibratethe system though not necessarily in the way predicted by standard open systemtechniques. Thus, we apply a novel technique called the Hilbert space AverageMethod (HAM) and verify its results numerically.Comment: 12 pages, 10 figure

Finite quantum environments as thermostats: an analysis based on the Hilbert space average method