  Two non-directly interacting qubits with equal frequencies can become
entangled via a Markovian, dissipative dynamics through the action of a weakly
coupled Ohmic heat bath. In the standard weak-coupling limit derivation, this
purely dissipative effect disappears if the frequencies are different because
of the "ergodic average" used by this approach. However, there are physical
situations where this technique is too rough to capture all the relevant
aspects of the dissipative dynamics. In these cases, in order to better
describe the physical behavior of the open system, it is necessary to go beyond
the "ergodic average". We show that, in this more refined framework, the
entanglement capability of the environment persists also in the case of
different frequencies.
