Similarity of extremely rare nonequilibrium processes to equilibrium processes

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. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a 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 ff_{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 Collapse

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Affiliation(s)

Peter Werner Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
Alexander K Hartmann Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
Satya N Majumdar Laboratoire de Physique Théorique et Modèles Statistique, Université Paris-Saclay, 91405 Orsay CEDEX, France

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Optimized finite-time work protocols for the Higgs RNA model with external force

The Higgs RNA model with an added term for a coupling to an external force is studied in regard to finite-time force-driving protocols with a minimal-work requirement. In this paper, RNA sequences which at low temperature exhibit hairpins are considered, which are often cited as typical template systems in stochastic thermodynamics. The optimized work protocols for this glassy many-particle system are determined numerically using the parallel tempering method. The protocols show distinct jumps at the beginning and end, which have been observed for single-particle systems and are proven to be optimal in the fast protocol limit generally. Optimality seems to be achieved by staying close to the equilibrium unfolding transition point, in agreement with experimental and theoretical observations. The change of work distributions, compared to those resulting from a naive linear driving protocol, are discussed generally and in terms of free energy estimation as well as the effect of optimized protocols on rare work process starting conditions.

Large deviations of a susceptible-infected-recovered model around the epidemic threshold

We numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum fraction of simultaneously infected nodes down to very small probability densities like 10^{-2500}. We analyze the structure of the disease dynamics and observed three regimes in all probability density functions, which correspond to quick mild, quick extremely severe, and sustained severe dynamical evolutions, respectively. Furthermore, the mathematical rate functions of the densities are investigated. The results indicate that the so-called large-deviation property holds for the SIR model. Finally, we measured correlations with other quantities like the duration of an outbreak or the peak position of the fraction of infections, also in the rare regions which are not accessible by standard simulation techniques.