  We analyze the behavior of a network of quantum oscillators coupled with a
number of external environments. We show that the dynamics is such that the
quantum state of the network always obeys a local master equation with a simple
analytical solution. We use this to study the emergence of thermodynamical laws
in the stationary regime, achieved for sufficiently long times if the
environments are dissipative. We show that the validity of the second law
implies the impossibility of building a quantum refrigerator without moving
parts (therefore, a quantum absorption refrigerators requires non-linearity as
an crucial ingredient, as recently proposed by Kosloff and others
cite{Kosloff1,Kosloff2}). We also show that the third law imposes strong
constraints on the low frequency behavior of the environmental spectral
densities.
