  We study analytically the dynamics of a generalized p-spin model, starting
with a thermalized initial condition. The model presents birth and death of
states, hence the dynamics (even starting at equilibrium) may go out of
equilibrium when the temperature is varied. We give a full description of this
constrained out of equilibrium behavior and we clarify the connection to the
thermodynamics by computing (sub-dominant) TAP states, constrained to the
starting equilibrium configuration.
