Entanglement generation in quantum thermal machines

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.