标题： 随机势垒穿越的时间尺度：从非平衡数据推断势能 显示英文标题

标题： Timescales for stochastic barrier crossing: inferring the potential from nonequilibrium data

摘要： 克雷默斯速率理论是热激活势垒穿越的基石。 然而，它依赖于平衡量，排除了对早期时间非平衡动力学的分析。 因此，大多数研究集中在获得平衡状态下的速率和过渡时间及路径分布。 相反，这里我们考虑一个粒子在双势阱势场中以阻尼动力学越过势垒的模型系统中的早期时间非平衡动力学，使用斯莫卢霍夫斯基方程（SE）和朗之万方程的随机路径积分（SPI）映射。 我们识别出几个与非平衡动力学相关的关键时间尺度，并使用SE和SPI方法对其进行量化。 最短的时间尺度对应于在时间$t \ll \tau_{\rm B}$时势阱内的平衡，其中$\tau_{\rm B}$是布朗扩散时间。 第二个重要的时间尺度是当从密度构建的有效势能中出现拐点的时间$t \lessapprox \tau_{\rm B}$。 不久之后，可以通过对动力学的充分采样推断出第二个势阱的存在。 有趣的是，这个时间尺度随着势垒高度的增加而减小。 除非$t \gg \tau_{\rm B}$，否则我们会发现与平衡极限有显著偏差。 我们进一步计算了双稳态和不对称势场中势垒处的\red{the}密度电流，并发现其在不依赖势垒高度的时间上会过渡到平衡速率理论的值。 我们的结果对在有限时间内控制激活过程具有重要意义，并展示了达到足够长的时间以从实验或模拟数据中准确构造势能景观的重要性。 显示英文摘要

摘要： Kramers' rate theory forms a cornerstone for thermally activated barrier crossing. However, its reliance on equilibrium quantities excludes analysis of nonequilibrium dynamics at early times. Most works have thus focused on obtaining rates and transition time and path distributions in equilibrium. Instead, here we consider early-time nonequilibrium dynamics in a model system of a particle with overdamped dynamics hopping over the barrier in a double-well potential, using the Smoluchowski equation (SE) and stochastic path integral (SPI) mapping of the Langevin equation. We identify several key timescales relevant to nonequilibrium dynamics and quantify them using the SE and SPI approaches. The shortest timescale corresponds to equilibration in a well at time $t \ll \tau_{\rm B}$, where $\tau_{\rm B}$ is the Brownian diffusion time. The second important timescale is when an inflexion point appears in the effective potential constructed from the density at $t \lessapprox \tau_{\rm B}$. Shortly after, the existence of a second potential well can be inferred from sufficient sampling of the dynamics. Interestingly, this timescale decreases with increasing barrier height. We find significant deviations from the equilibrium limit unless $t \gg \tau_{\rm B}$. We further calculate \red{the} density current at the barrier for bistable and asymmetric potentials and find that it crosses over to that from equilibrium rate theory at a time that does not appear to depend on the barrier height. Our results have important implications for controlling activated processes at finite times and demonstrate the importance of reaching long enough times to faithfully construct potential landscapes from experimental or simulation data.