  It is common knowledge that coupling to a heat bath, in general, tends to
reduce the entanglement in a quantum system. In recent years, increasing
interest has been devoted to the opposite situation where thermal or
specifically tailored environments may stabilize or even generate entanglement.
We prove the universality of this phenomenon for multipartite entanglement in
the frame of an exactly solvable dephasing model. We show by evaluating
analytical lower bounds for the appropriate entanglement measures that a common
thermal environment can dynamically generate all entanglement classes of three
qubits for almost any initial product state. For sufficiently weak dissipation
this entanglement may persist up to arbitrarily large times.
