  In the framework of the theory of open systems based on completely positive
quantum dynamical semigroups, we give a description of the dynamics of
entanglement for a system consisting of two uncoupled harmonic oscillators
interacting with a thermal environment. Using 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 a Gaussian
input state. For some values of the temperature of environment, the state keeps
for all times its initial type: separable or entangled. In other cases,
entanglement generation, entanglement sudden death or a repeated collapse and
revival of entanglement take place. We determine the asymptotic Gaussian
maximally entangled mixed states (GMEMS) and their corresponding asymptotic
maximal logarithmic negativity.
