The non-classical kinetics and the mutual information of polymer loop formation

The loop formation of a single polymer chain has served as a model system for various biological and chemical processes. Theories based on the Smoluchowski equation proposed that the rate constant (k_loop) of the loop formation would be inversely proportional to viscosity (η), i.e., k_loop ∼ η^-1. Experiments and simulations showed, however, that k_loop showed the fractional viscosity dependence of k_loop ∼ η^-β with β < 1 either in glasses or in low-viscosity solutions. The origin of the fractional viscosity dependence remains elusive and has been attributed to phenomenological aspects. In this paper, we illustrate that the well-known failure of classical kinetics of the loop formation results from the breakdown of the local thermal equilibrium (LTE) approximation and that the mutual information can quantify the breakdown of the LTE successfully.