  We derive the differential equation describing the time evolution of the work
probability distribution function of a stochastic system which is driven out of
equilibrium by the manipulation of a parameter. We consider both systems
described by their microscopic state or by a collective variable which
identifies a quasiequilibrium state. We show that the work probability
distribution can be represented by a path integral, which is dominated by
``classical'' paths in the large system size limit. We compare these results
with simulated manipulation of mean-field systems. We discuss the range of
applicability of the Jarzynski equality for evaluating the system free energy
using these out-of-equilibrium manipulations. Large fluctuations in the work
and the shape of the work distribution tails are also discussed.
