  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 independent harmonic oscillators
interacting with a general environment. Using Peres-Simon necessary and
sufficient criterion for separability of two-mode Gaussian states, we describe
the generation and evolution of entanglement in terms of the covariance matrix
for an arbitrary Gaussian input state. For some values of diffusion and
dissipation coefficients describing the environment, the state keeps for all
times its initial type: separable or entangled. In other cases, entanglement
generation or entanglement collapse (entanglement sudden death) take place or
even a periodic collapse and revival of entanglement. 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.
