Decoherence and equilibration under nondestructive measurements
  The evolution of observable quantities of finite quantum systems is analyzed when the latter are subject to nondestructive measurements. The type and number of measurements characterize the level of decoherence produced in the system. A finite number of instantaneous measurements leads to only a partial decoherence. But infinite number of such measurements yields complete decoherence and equilibration. Continuous measurements result in partial decoherence in finite time, but produce complete decoherence and equilibration as time tends to infinity. Resulting equilibrium states are characterized by representative statistical ensembles that, generally, retain information on initial conditions. Any system, to be observable, necessarily requires the presence of measurements, whose large number leads to the system equilibration and decoherence. 
V. I. Yukalov
quant-ph cond-mat.stat-mech