Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture
Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture
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DOI：
10.1063/1.5120511
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发表时间：
2019-11-07
影响因子：
4.4
通讯作者：
Zuckerman, Daniel M.
中科院分区：
文献类型：
--
作者：
Copperman, Jeremy;Aristoff, David;Zuckerman, Daniel M.
概率流是描述非平衡过程动力学的基本方法。值得注意的是，源-宿系统的稳态电流J（ss）可以为从源到宿的过渡提供精确的平均首次通过时间（MFPT）。由于瞬态非平衡行为是量化的一些现代的路径采样方法，如“加权合奏”的战略，有强烈的动机，以确定界限J（SS），因此对MFPT系统的演变时间。在这里，我们证明了J（ss）分别由电流的最大值和最小值从上到下有界，该电流作为经历过阻尼朗之万的一维系统在任何时间t的空间坐标的函数（即，Smoluchowski）动力学以及投影到一维时满足某些假设的高维Smoluchowski系统。随着时间的推移，这些界限变得更紧，使它们在估计J（SS）和复杂系统的长时间尺度动力学的计划中具有潜在的实际效用。从概念上讲，边界是由于瞬时电流的极值向稳态电流放松这一事实而产生的。
Probability currents are fundamental in characterizing the kinetics of nonequilibrium processes. Notably, the steady-state current J(ss) for a source-sink system can provide the exact mean-first-passage time (MFPT) for the transition from the source to sink. Because transient nonequilibrium behavior is quantified in some modern path sampling approaches, such as the "weighted ensemble" strategy, there is strong motivation to determine bounds on J(ss)-and hence on the MFPT-as the system evolves in time. Here, we show that J(ss) is bounded from above and below by the maximum and minimum, respectively, of the current as a function of the spatial coordinate at any time t for one-dimensional systems undergoing overdamped Langevin (i.e., Smoluchowski) dynamics and for higher-dimensional Smoluchowski systems satisfying certain assumptions when projected onto a single dimension. These bounds become tighter with time, making them of potential practical utility in a scheme for estimating J(ss) and the long time scale kinetics of complex systems. Conceptually, the bounds result from the fact that extrema of the transient currents relax toward the steady-state current.