Hi ChenJi,
One standard way to determine if a system has attained equilibrium is to compute the time-autocorrelation function C_X (t) of a random variable X (e.g. the energy). C(t) should be of an exponential form (if there is a single timescale in the process), having a relaxation time \tau. Due to the properties of the exponential, \tau can be expressed as a time integral of C. This is a way to get a precise number for the relaxation time, but it is also fairly tedious. Usually you’re pretty sure to be in equilibrium once C gets “close” to zero.
Andy