  In the framework of the theory of open systems based on completely positive
quantum dynamical semigroups, we solve in the asymptotic long-time regime the
master equation for two independent harmonic oscillators interacting with an
environment. We give a description of the continuous-variable asymptotic
entanglement in terms of the covariance matrix of the considered subsystem for
an arbitrary Gaussian input state. Using Peres--Simon necessary and sufficient
condition for separability of two-mode Gaussian states, we show that for
certain classes of environments the initial state evolves asymptotically to an
entangled equilibrium bipartite state, while for other values of the
coefficients describing the environment, the asymptotic state is separable. We
calculate also the logarithmic negativity characterizing the degree of
entanglement of the asymptotic state.
