论文标题
不可逆动力学中的过渡路径的元动力学
Metadynamics for transition paths in irreversible dynamics
论文作者
论文摘要
随机系统通常表现出多种可行的亚稳态状态，这些状态是长寿的。在很长的时间尺度上，波动可能会推动系统之间的过渡，从而极大地改变了其宏观配置。在现实的系统中，这些过渡可以通过多种物理机制进行，这对应于一对状态的多个不同的过渡通道。在本文中，我们使用这样一个事实，即过渡路径集合相当于路径空间中梯度流的不变度度量，该梯度流可以通过元动力学有效地采样。我们演示了这种路径空间元动力学如何限于可逆分子动力学，实际上通常非常适用于可稳态的随机系统，包括不可逆和时间依赖性的系统，并允许严格估算竞争过渡路径的相对可能性。我们在研究中描述磁场逆转的随机部分微分方程的研究中展示了这种方法。
Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic systems, these transitions can happen via multiple physical mechanisms, corresponding to multiple distinct transition channels for a pair of states. In this paper, we use the fact that the transition path ensemble is equivalent to the invariant measure of a gradient flow in pathspace, which can be efficiently sampled via metadynamics. We demonstrate how this pathspace metadynamics, previously restricted to reversible molecular dynamics, is in fact very generally applicable to metastable stochastic systems, including irreversible and time-dependent ones, and allows to estimate rigorously the relative probability of competing transition paths. We showcase this approach on the study of a stochastic partial differential equation describing magnetic field reversal in the presence of advection.
