In this article we review the foundations of dynamical description of
unstable systems. We describe the concept of stochastic one-body theor
ies. In particular, spinodal instabilities are accounted for: the most
unstable modes which depend mostly on the range of the nuclear force
are shown to determine the early unstable dynamics and therefore the i
nitial multifragmentation; the characteristic time scales for the grow
th of these modes and the typical time scales for cluster formation, a
s a function of the amplitude of fluctuations, are discussed. The diff
erences between such a fragmentation pattern, essentially determined b
y the instabilities, and fragmentation structures obtained from the hy
pothesis of statistical equilibrium are stressed. Finally, we propose
that the occurrence of spinodal instabilities can be signed by a lack
of small size fragments associated to a tendency to break the system i
n close-mass pieces.