I will describe the dynamics of classical disordered macroscopic models
(of p-spin kind) completely isolated from any environment in a classical
setting that reproduces the "quantum quench" protocol. The asymptotic
dynamics can reach a steady state of Gibbs-Boltzmann kind for
non-integrable (p > 2, multi-body) interactions while, instead, they
approach a stationary state of Generalized Gibbs Boltzmann type in
integrable (p = 2, two-body) cases. Interesting phase transitions will be
discussed in both cases. Methods to sample efficiently the asymptotic
measures will also be discussed. This talk summarizes work done in
collaboration with D. Barbier, R. Gonzalez-Albaladejo, G. Lozano, N.
Nessi, M. Picco, D. Stariolo, and A. Tartaglia.