  In entangled polymer systems, there are several characteristic time scales,
such as the entanglement time and the disengagement time. In molecular
simulations, the longest relaxation time (the disengagement time) can be
determined by the mean square displacement (MSD) of a segment or by the shear
relaxation modulus. Here, we propose the relative fluctuation analysis method,
which is originally developed for characterizing large fluctuations, to
determine the longest relaxation time from the center of mass trajectories of
polymer chains (the time-averaged MSDs). Applying the method to simulation data
of entangled polymers (by the slip-spring model and the simple reptation
model), we provide a clear evidence that the longest relaxation time is
estimated as the crossover time in the relative fluctuations.
