  We study entanglement dynamics in quantum Brownian motion (QBM) models. Our
main tool is the Wigner function propagator. Time evolution in the Wigner
picture is physically intuitive and it leads to a simple derivation of a master
equation for any number of system harmonic oscillators and spectral density of
the environment. It also provides generalized uncertainty relations, valid for
any initial state that allow a characterization of the environment in terms of
the modifications it causes to the system's dynamics. In particular, the
uncertainty relations are very informative about the entanglement dynamics of
Gaussian states, and to a lesser extent for other families of states. For
concreteness, we apply these techniques to a bipartite QBM model, describing
the processes of entanglement creation, disentanglement and decoherence at all
temperatures and timescales.
