Brownian non-Gaussian polymer diffusion and queuing theory in the mean-field limit

We link the Brownian non-Gaussian diffusion of a polymer center of mass (CM) 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 CM 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.

Automated summary

We investigate the anomalous behavior of the Brownian non-Gaussian diffusion of a polymer center of mass (CM) and its microscopic cause, the polymerization/depolymerization phenomenon, when the polymer interacts with a monomer chemostat. We establish a connection to queuing theory in the mean-field limit and discover that the kurtosis of the polymer CM diverges similarly to a response function at the critical point of the system, which is applicable to various polymer dynamics models. This study provides exact solutions for both equilibrium and nonequilibrium behaviors, serving as a reference for stochastic modeling and experimental setups.