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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 strandedhairpin is connected to a heat bath at temperature $T$ and subject to anexternal force $f$, which couples to the free length $L$ of the unzippedsequence. Increasing the force, leads to an zipping/unzipping first-order phasetransition at a critical force $f_c(T)$ in the thermodynamic limit of a verylarge chain. We compute analytically, as a function of temperature $T$ andforce $f$, the full distribution $P(L)$ of free lengths in the thermodynamiclimit 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 isincremented according to a linear protocol. Having obtained $P(L)$ alreadyallows 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-deviationtails of the work distribution explicitly. Our analytical result for the workdistribution is compared over a large range of the support down toprobabilities as small as $10^{-200}$ with numerical simulations, which wereperformed by applying sophisticated large-deviation algorithms.

Work Distribution for Unzipping Processes