  We link the Brownian non-Gaussian diffusion of a polymer center of mass to a
microscopic cause: the polymerization/depolymerization phenomenon occurring
when the polymer is in contact with a monomer chemostat. The anomalous behavior
is triggered by the polymer critical point, separating the dilute and the dense
phase in the grand canonical ensemble. In the mean-field limit we establish
contact with queuing theory and show that the kurtosis of the polymer center of
mass diverges alike a response function when the system becomes critical, a
result which holds for general polymer dynamics (Zimm, Rouse, reptation). Both
the equilibrium and nonequilibrium behaviors are solved exactly as a reference
study for novel stochastic modeling and experimental setup.

Statistical Mechanics;Soft Condensed Matter