  We propose a method to detect possible non-stationarities of gamma-ray burst
jets. Assuming that the dominant source of variability in the prompt gamma
light curve is the non-stationarity of the jet, we show that there should be a
connection between the variability measure and the characteristic angle of the
jet derived from the jet break time of the afterglow. We carried out Monte
Carlo simulations of long gamma-ray burst observations assuming three radial
luminosity density profiles for jets and randomizing all burst parameters, and
created samples of gamma light curves by simulating jets undergoing Brownian
motions with linear restoring forces. We were able to demonstrate that the
connection between the variability and the characteristic angle is an
anti-correlation in case of uniform and power-law jet profiles, and a
correlation in case of a Gaussian profile. We have found that as low as $50$
$(144)$ gamma-ray burst observations with jet angle measurements can be
sufficient for a $3\sigma\ (5\sigma) $ detection of the connection. The number
of observations required for the detection depends on the underlying jet beam
profile, ranging from 50 (144) to 237 (659) for the four specific profile
models we tested.
