  In the framework of the theory of open systems based on completely positive
quantum dynamical semigroups, we give a description of the continuous-variable
entanglement for a system consisting of two noninteracting modes embedded in a
thermal environment. By using the Peres-Simon necessary and sufficient
criterion for separability of two-mode Gaussian states, we describe the
evolution of entanglement in terms of the covariance matrix for Gaussian input
states. For all values of the temperature of the thermal reservoir, an initial
separable Gaussian state remains separable for all times. In the case of an
entangled initial Gaussian state, entanglement suppression (entanglement sudden
death) takes place, for non-zero temperatures of the environment. Only for a
zero temperature of the thermal bath the initial entangled state remains
entangled for finite times. We also show that, independent of its type -
separable or entangled, the initial state evolves asymptotically to an
equilibrium state which is always separable.
