Journal article
Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture
The Journal of chemical physics, v 151(17), pp 174108-174108
07 Nov 2019
PMID: 31703496
Featured in Collection : UN Sustainable Development Goals @ Drexel
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.
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Details
- Title
- Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture
- Creators
- Jeremy Copperman - Oregon Health & Science UniversityDavid Aristoff - Colorado State UniversityDmitrii E. Makarov - The University of Texas at AustinGideon Simpson - Drexel UniversityDaniel M. Zuckerman - Oregon Health & Science University
- Publication Details
- The Journal of chemical physics, v 151(17), pp 174108-174108
- Publisher
- American Institute of Physics
- Number of pages
- 12
- Grant note
- R01GM115805 / NATIONAL INSTITUTE OF GENERAL MEDICAL SCIENCES; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA; NIH National Institute of General Medical Sciences (NIGMS) GM115805 / NIH; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA F-1514 / Robert A. Welch Foundation; The Welch Foundation CHE-1566001; DMS-1522398; DMS-1818726 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000496485600028
- Scopus ID
- 2-s2.0-85074696988
- Other Identifier
- 991019168676204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Chemistry, Physical
- Physics, Atomic, Molecular & Chemical