  We investigate the routes by which a bath composed of a finite number of
oscillators at zero temperature approaches the induction of dissipation when it
nears the usual limit of dense spectrum spread in an infinite interval. It is
shown that, when this limit is taken, different distributions of environment
frequencies can lead to the same irreversible evolution. However, when we move
away from it, the dynamics departs from irreversibility in qualitatively
different manners.
