Work distribution functions in polymer stretching experiments

We compute the distribution of the work done in stretching a Gaussian polymer, made of $N$ monomers, at a finite rate. For a one-dimensional polymer undergoing Rouse dynamics, the work distribution is a Gaussian and we explicitly compute the mean and width. The two cases where the polymer is stretched, either by constraining its end or by constraining the force on it, are examined. We discuss connections to Jarzynski’s equality and the fluctuation theorems.

Figure 1

Distributions of the work done in pulling a short polymer $(N=1)$ at different rates $r={\tau }_R∕{\tau }_m$.

Figure 2

Distributions of the work done in pulling a long polymer $(N=100)$ at different rates $r={\tau }_R∕{\tau }_m$.