  We use the quantum Brownian model to derive the uncertainty relation for a
quantum open system. We examine how the fluctuations of a quantum system evolve
after it is brought in contact with a heat bath at finite temperature. We study
the decoherence and relaxation processes and use this example to examine 1) the
relation between quantum and thermal fluctuations; and 2) the conditions when
the two basic postulates of quantum statistical mechanics become valid.
