Uncertainty Relation at Finite Temperature

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.