  The von Neumann entropy of various quantum dissipative models is calculated
in order to discuss the entanglement properties of these systems. First,
integrable quantum dissipative models are discussed, i.e., the quantum Brownian
motion and the quantum harmonic oscillator. In case of the free particle, the
related entanglement of formation shows no non-analyticity. In case of the
dissipative harmonic oscillator, there is a non-analyticity at the transition
of underdamped to overdamped oscillations. We argue that this might be a
general property of dissipative systems. We show that similar features arise in
the dissipative two level system and study different regimes using sub-Ohmic,
Ohmic and and super-Ohmic baths, within a scaling approach.
