  We study a chain of identical glassy systems in a constrained equilibrium
where each bond of the chain is forced to remain at a preassigned distance to
the previous one. We apply this description to Mean Field Glassy systems in the
limit of long chain where each bond is close to the previous one. We show that
in specific conditions this pseudo-dynamic process can formally describe real
relaxational dynamics the long time. In particular, in mean field spin glass
models we can recover in this way the equations of Langevin dynamics in the
long time limit at the dynamical transition temperature and below. We interpret
the formal identity as an evidence that in these situations the configuration
space is explored in a quasi-equilibrium fashion. Our general formalism, that
relates dynamics to equilibrium puts slow dynamics in a new perspective and
opens the way to the computation of new dynamical quantities in glassy systems.
