Extremely quick thermalization in a macroscopic quantum system for a   typical nonequilibrium subspace
  The fact that macroscopic systems approach thermal equilibrium may seem puzzling, for example, because it may seem to conflict with the time-reversibility of the microscopic dynamics. We here prove that in a macroscopic quantum system for a typical choice of "nonequilibrium subspace", any initial state indeed thermalizes, and in fact does so very quickly, on the order of the Boltzmann time $\tau_\mathrm{B}:=h/(k_\mathrm{B}T)$. Therefore what needs to be explained is, not that macroscopic systems approach equilibrium, but that they do so slowly. 
Sheldon Goldstein, Takashi Hara, and Hal Tasaki
cond-mat.stat-mech math-ph math.MP quant-ph