Aging and Effective Temperatures in the Low Temperature Mode-Coupling Equations

The low-temperature generalization of the mode-coupling equations corresponds to the dynamics of mean-field disordered models in the glassy phase. The system never achieves equilibrium, preserving the memory of the time elapsed after the quench throughout its evolution. A concept of effective temperature can be made quite rigorous in this context by considering readings of thermometers in different time-scales and the thermalization of weakly coupled subsystems.