  We investigate the nonequilibrium tube length fluctuations during the
relaxation of an initially stretched, entangled polymer chain. The
time-dependent variance $\sigma^2$ of the tube length follows in the early-time
regime a simple universal power law $\sigma^2 = A \sqrt{t}$ originating in the
diffusive motion of the polymer segments. The amplitude $A$ is calculated
analytically both from standard reptation theory and from an exactly solvable
lattice gas model for reptation and its dependence on the initial and
equilibrium tube length respectively is discussed. The non-universality
suggests the measurement of the fluctuations (e.g. using flourescence
microscopy) as a test for reptation models.
