  The exact evolution of a system coupled to a complex environment can be
described by a stochastic mean-field evolution of the reduced system density.
The formalism developed in Ref. [D.Lacroix, Phys. Rev. E77, 041126 (2008)] is
illustrated in the Caldeira-Leggett model where a harmonic oscillator is
coupled to a bath of harmonic oscillators. Similar exact reformulation could be
used to extend mean-field transport theories in Many-body systems and
incorporate two-body correlations beyond the mean-field one. The connection
between open quantum system and closed many-body problem is discussed.
