Off-equilibrium confined dynamics in a glassy system with level-crossing   states
  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. 
Barbara Capone, Tommaso Castellani, Irene Giardina, Federico   Ricci-Tersenghi