### Abstract

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.

Original language | English (US) |
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Article number | 5120511 |

Journal | Journal of Chemical Physics |

Volume | 151 |

Issue number | 17 |

DOIs | |

State | Published - Nov 7 2019 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

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## Cite this

*Journal of Chemical Physics*,

*151*(17), [5120511]. https://doi.org/10.1063/1.5120511