Fundamental limits for cooling of linear quantum refrigerators

We study the asymptotic dynamics of arbitrary linear quantum open systems which are periodically driven while coupled with generic bosonic reservoirs. We obtain exact results for the heat flowing into the network, which are valid beyond the usual weak coupling or Markovian approximations. We prove the validity of the dynamical third law of thermodynamics (Nernst unattainability principle), showing that the ultimate limit for cooling is imposed by a fundamental heating mechanism which becomes dominant at low temperatures: the non resonant creation of pairs of excitations in the reservoirs induced by the driving field. This quantum effect, which is missed in the weak coupling approximation, restores the unattainability principle whose validity was recently challenged.