Nonequilibrium interactions between ideal polymers and a repulsive surface

We use Newtonian and overdamped Langevin dynamics to study long flexible polymers dragged by an external force at a constant velocity v. The work W performed by that force depends on the initial state of the polymer and the details of the process. The Jarzynski equality can be used to relate the nonequilibrium work distribution P(W) obtained from repeated experiments to the equilibrium free energy difference ΔF between the initial and final states. We use the power law dependence of the geometrical and dynamical characteristics of the polymer on the number of monomers N to suggest the existence of a critical velocity vc(N), such that for v<vc the reconstruction of ΔF is an easy task, while for v significantly exceeding vc it becomes practically impossible. We demonstrate the existence of such vc analytically for an ideal polymer in free space and numerically for a polymer which is being dragged away from a repulsive wall. Our results suggest that the distribution of the dissipated work Wd=W-ΔF in properly scaled variables approaches a limiting shape for large N.