Work Distribution for Unzipping Processes

A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature $T$ and subject to an external force $f$, which couples to the free length $L$ of the unzipped sequence. Increasing the force, leads to an zipping/unzipping first-order phase transition at a critical force $f_c(T)$ in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature $T$ and force $f$, the full distribution $P(L)$ of free lengths in the thermodynamic limit and show that it is qualitatively very different for $f<f_c$, $f=f_c$ and $f>f_c$. Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained $P(L)$ already allows us to derive an analytical expression for the work distribution $P(W)$ in the zipped phase $f<f_c$ for a long chain. We compute the large-deviation tails of the work distribution explicitly. Our analytical result for the work distribution is compared over a large range of the support down to probabilities as small as $10^{-200}$ with numerical simulations, which were performed by applying sophisticated large-deviation algorithms.