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Relaxation to equilibrium in the random energy model is investigated with the use of the master equation within the assumption that transition state between any two energy levels has the same energy. Relaxation of physical quantities of the model after drastic decrease of temperature is a two-stage process when final temperature is lower than the temperature of freezing transition. At the first stage there occurs a logarithmic relaxation of the extensive part of energy to equilibrium (in the thermodynamic limit) value. The second stage is connected with the freezing transition.
Shakhnovich et al. (1989) studied this question.