We consider several cases of an ideal polymer being dragged by an external force. The work W in such a process depends on the initial state of the polymer. If the initial state is selected from a canonical ensemble, then the distribution of (non-equilibrium) W can be related to the difference in the free energy ∆F between the initial and the (equilibrated) final states by the means of Jarzynski equality (JE) [1]. We consider either Newtonian dynamics or over-damped Langevin equations, for a polymer that is moving in a free space or is initially located near a repulsive wall. In all cases the end of a polymer is dragged with a constant velocity.

We reconstruct (either analytically or numerically) the distribution of W, and demonstrate that there is critical velocity v_c such that for v<v_c  the ∆F can be easily reconstructed, while for v>>v_c  such reconstruction is, practically, impossible. We determine the dependence of v_c  on the number of monomers and other parameters of the problem. The interaction between the polymer and the repulsive wall during the (non-equilibrium) motion of the polymer is measured for various velocities.

[1] C. Jarzynski, Phys. Rev. Lett.  78, 2690 (1997).