  The method of positive commutators, developed for zero temperature problems
over the last twenty years, has been an essential tool in the spectral analysis
of Hamiltonians in quantum mechanics. We extend this method to positive
temperatures, i.e. to non-equilibrium quantum statistical mechanics.
  We use the positive commutator technique to give an alternative proof of a
fundamental property of a certain class of large quantum systems, called {\it
Return to Equilibrium}. This property says that equilibrium states are
(asymptotically) stable: if a system is slightly perturbed from its equilibrium
state, then it converges back to that equilibrium state as time goes to
infinity.
