  We show that in a linear quantum machine, a driven quantum system that
evolves while coupled with thermal reservoirs, entanglement between the
reservoir modes is unavoidably generated. This phenomenon, which occurs at
sufficiently low temperatures and is at the heart of the third law of
thermodynamics, is a consequence of a simple process: the transformation of the
energy of the driving field into pairs of excitations in the reservoirs. For a
driving with frequency $\omega_{d}$ we show entanglement exists between
environmental modes whose frequencies satisfy the condition $\omega_{i} +
\omega_{j}= \omega_{d}$. We show that this entanglement can persist for
temperatures that can be significantly higher than the lowest achievable ones
with sideband resolved cooling methods.
