Squeezed States and Uncertainty Relation at Finite Temperature

We use the quantum Brownian model to derive the uncertainty relation for a quantum open system in an arbitrarily-squeezed initial state interacting with an environment at finite temperature. We examine the relative importance of the quantum and thermal fluctuations in the evolution of the system towards equilibrium with the aim of clarifying the meaning of quantum, classical and thermal. We show that upon contact with the bath the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is the same as the decoherence time calculated before in the context of quantum to classical transitions. We also use these results to deduce the conditions when the two basic postulates of quantum statistical mechanics become valid.