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

TL;DR

This paper connects non-Gaussian polymer diffusion to microscopic polymerization phenomena, revealing critical behavior and divergence in kurtosis through mean-field and queuing theory analysis, applicable to various polymer dynamics.

Contribution

It introduces a novel link between polymer non-Gaussian diffusion and queuing theory, providing exact solutions for equilibrium and nonequilibrium behaviors at the critical point.

Findings

Kurtosis diverges at the critical point, indicating phase transition.

Exact solutions for polymer dynamics in both equilibrium and nonequilibrium states.

Universal behavior across different polymer models like Zimm, Rouse, and reptation.

Abstract

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.