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 $W$ by that force depends on the initial state of the polymer and the details of the process. Jarzynski equality can be used to relate the non-equilibrium work distribution $P(W)$ obtained from repeated experiments to equilibrium free energy difference $\Delta F$ 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 $v_c(N)$, such that for $v<v_c$ the reconstruction of $\Delta F$ is an easy task, while for $v$ significantly exceeding $v_c$ it becomes practically impossible. We demonstrate the existence of such $v_c$ analytically for ideal polymer in free space and numerically for a polymer being dragged away from a repulsive wall. Our results suggest that the distribution of the dissipated work $W_{\rm d}=W-\Delta F$ in properly scaled variables approaches a limiting shape for large $N$.