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

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.

arXiv comment18 pages, 7 figures

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• A non-homogeneous, non-stationary and path-dependent Markov anomalous diffusion model
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• Beyond the Big Jump: A Perturbative Approach to Stretched-Exponential Processes