Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture

Jeremy Copperman, David Aristoff, Dmitrii E. Makarov, Gideon Simpson, Daniel M. Zuckerman

Research output: Contribution to journalArticle

Abstract

Probability currents are fundamental in characterizing the kinetics of nonequilibrium processes. Notably, the steady-state current Jss 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 Jss - and hence on the MFPT - as the system evolves in time. Here, we show that Jss 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 Jss 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 languageEnglish (US)
Article number5120511
JournalJournal of Chemical Physics
Volume151
Issue number17
DOIs
StatePublished - Nov 7 2019

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Kinetics
Large scale systems
Sampling
sinks
kinetics
range (extremes)
complex systems
estimating
sampling

ASJC Scopus subject areas

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

Cite this

Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture. / Copperman, Jeremy; Aristoff, David; Makarov, Dmitrii E.; Simpson, Gideon; Zuckerman, Daniel M.

In: Journal of Chemical Physics, Vol. 151, No. 17, 5120511, 07.11.2019.

Research output: Contribution to journalArticle

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