Abstract: In this paper, we generalize Freidlin and Wentzell machinery[7] to the case of Glauber dynamics, which is still a stochastic dynamics even as the temperature vanishes. We first consider the probability to exit from an attractive basin and enter into another one in the limit as the temperature goes to zero. The first exiting time to escape from an attractive basin of an attractor in which the process starts is estimated. Then we show conclusions above in the case of exiting from a region formed by several attractive basins. The unpredictability of the exiting time is proved.

Key words: Glauber dynamics, Attractor, Attractive basin, Essential attractive basin, Exiting time, most possible path