Decoherence and Irreversibility: the role of the reservoir effective   Hilbert space size
  We show that decoherence is determined by the effective Hilbert space size, and demonstrate that a few degrees of freedom system can simulate a "N" degrees of freedom environment if they have the same effective Hilbert space. The effective Hilbert space size of the environment also determines its long time efficiency as generator of irreversible coherence loss. 
Adelcio C. Oliveira and A. R. Bosco de Magalhaes