For system coupled to heat baths, typical nonequilibrated processes, e.g., induced by varying an external parameter without waiting for equilibration in between, are very different from the corresponding equilibrium infinitely slow processes. Nevertheless, there are connections between equilibrium and nonequilibrated behaviors, e.g., the theorems of Jarzynski and Crooks, which relate the distribution $P\left(W\right)$ of nonequilibrium work to the free energy differences $\mathrm{\Delta }F$. Here we study the naturally arising question, whether those relevant but rare trajectories, which exhibit these work values, show a higher degree of similarity to equilibrium. For convenience, we have chosen a simple model of RNA secondary structures (or single-stranded DNA), here modeling a medium-size hairpin structure, under influence of a varying external force. This allows us to measure the work $W$ during the resulting fast unfolding and refolding processes within Monte Carlo simulations, i.e., in nonequilibrium. Also we sample numerically efficiently directly in exact equilibrium, for comparison. Using a sophisticated large-deviation algorithm, we are able to measure work distributions with high precision down to probabilities as small as ${10}^{-46}$, enabling us to verify the Crooks and Jarzynski theorems. Furthermore, we analyze force-extension curves and the configurations of the secondary structures during unfolding and refolding for typical equilibrium processes and nonequilibrated processes. We find that the nonequilibrated processes where the work values are close to those which are most relevant for applying Crooks and Jarzynski theorems, respectively, but which occur with exponential small probabilities, are most and quite similar to the equilibrium processes.

中文翻译：

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极其罕见的非平衡过程与平衡过程的相似性

对于耦合到热浴的系统，典型的非平衡过程，例如，通过改变外部参数而不等待两者之间的平衡引起的，与相应的无限缓慢过程非常不同。然而，均衡行为和非均衡行为之间存在联系，例如 Jarzynski 和 Crooks 的定理，它们将分布与$磷\left(宽\right)$ 非平衡功对自由能差异的影响 $\mathrm{\Delta }F$. 在这里，我们研究自然产生的问题，即表现出这些工作价值的那些相关但罕见的轨迹是否显示出与均衡的更高程度的相似性。为方便起见，我们选择了一个简单的 RNA 二级结构（或单链 DNA）模型，在此建模中等大小的发夹结构，受不同外力的影响。这使我们能够衡量工作$宽$在蒙特卡罗模拟中产生的快速展开和重折叠过程中，即处于非平衡状态。此外，我们直接在精确平衡中有效地进行数值采样，以进行比较。使用复杂的大偏差算法，我们能够以高精度测量工作分布，小至概率${10}^{-46}$，使我们能够验证 Crooks 和 Jarzynski 定理。此外，我们分析了典型平衡过程和非平衡过程的展开和重折叠过程中的力-延伸曲线和二级结构的配置。我们发现，工作值分别接近与应用 Crooks 和 Jarzynski 定理最相关的那些非平衡过程，但以指数小概率发生，与平衡过程最相似，非常相似。