  We consider a mean-field system described by a general collective variable
$M$, driven out of equilibrium by the manipulation of a parameter $\mu$. Given
a general dynamics compatible with its equilibrium distribution, we derive the
evolution equation for the joint probability distribution function of $M$ and
the work $W$ done on the system. We solve this equation by path integrals. We
show how the Jarzynski equality holds identically at the path integral level
and for the classical paths which dominate the expression in the thermodynamic
limit. We discuss some implications of our results.
