Metabasin approach for computing the master equation dynamics of systems with broken ergodicity

John C. Mauro, Roger J. Loucks, Prabhat K. Gupta

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

We propose a technique for computing the master equation dynamics of systems with broken ergodicity. The technique involves a partitioning of the system into components, or metabasins, where the relaxation times within a metabasin are short compared to an observation time scale. In this manner, equilibrium statistical mechanics is assumed within each metabasin, and the intermetabasin dynamics are computed using a reduced set of master equations. The number of metabasins depends upon both the temperature of the system and its derivative with respect to time. With this technique, the integration time step of the master equations is governed by the observation time scale rather than the fastest transition time between basins. We illustrate the technique using a simple model landscape with seven basins and show validation against direct Euler integration. Finally, we demonstrate the use of the technique for a realistic glass-forming system (viz., selenium) where direct Euler integration is not computationally feasible.

Original languageEnglish (US)
Pages (from-to)7957-7965
Number of pages9
JournalJournal of Physical Chemistry A
Volume111
Issue number32
DOIs
StatePublished - Aug 16 2007

Fingerprint

Statistical mechanics
Selenium
Relaxation time
Derivatives
Glass
selenium
statistical mechanics
Temperature
relaxation time
glass
temperature

All Science Journal Classification (ASJC) codes

  • Physical and Theoretical Chemistry

Cite this

@article{ce076411315d4ac6955bbccad0a070bd,
title = "Metabasin approach for computing the master equation dynamics of systems with broken ergodicity",
abstract = "We propose a technique for computing the master equation dynamics of systems with broken ergodicity. The technique involves a partitioning of the system into components, or metabasins, where the relaxation times within a metabasin are short compared to an observation time scale. In this manner, equilibrium statistical mechanics is assumed within each metabasin, and the intermetabasin dynamics are computed using a reduced set of master equations. The number of metabasins depends upon both the temperature of the system and its derivative with respect to time. With this technique, the integration time step of the master equations is governed by the observation time scale rather than the fastest transition time between basins. We illustrate the technique using a simple model landscape with seven basins and show validation against direct Euler integration. Finally, we demonstrate the use of the technique for a realistic glass-forming system (viz., selenium) where direct Euler integration is not computationally feasible.",
author = "Mauro, {John C.} and Loucks, {Roger J.} and Gupta, {Prabhat K.}",
year = "2007",
month = "8",
day = "16",
doi = "10.1021/jp0731194",
language = "English (US)",
volume = "111",
pages = "7957--7965",
journal = "Journal of Physical Chemistry A",
issn = "1089-5639",
publisher = "American Chemical Society",
number = "32",

}

Metabasin approach for computing the master equation dynamics of systems with broken ergodicity. / Mauro, John C.; Loucks, Roger J.; Gupta, Prabhat K.

In: Journal of Physical Chemistry A, Vol. 111, No. 32, 16.08.2007, p. 7957-7965.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Metabasin approach for computing the master equation dynamics of systems with broken ergodicity

AU - Mauro, John C.

AU - Loucks, Roger J.

AU - Gupta, Prabhat K.

PY - 2007/8/16

Y1 - 2007/8/16

N2 - We propose a technique for computing the master equation dynamics of systems with broken ergodicity. The technique involves a partitioning of the system into components, or metabasins, where the relaxation times within a metabasin are short compared to an observation time scale. In this manner, equilibrium statistical mechanics is assumed within each metabasin, and the intermetabasin dynamics are computed using a reduced set of master equations. The number of metabasins depends upon both the temperature of the system and its derivative with respect to time. With this technique, the integration time step of the master equations is governed by the observation time scale rather than the fastest transition time between basins. We illustrate the technique using a simple model landscape with seven basins and show validation against direct Euler integration. Finally, we demonstrate the use of the technique for a realistic glass-forming system (viz., selenium) where direct Euler integration is not computationally feasible.

AB - We propose a technique for computing the master equation dynamics of systems with broken ergodicity. The technique involves a partitioning of the system into components, or metabasins, where the relaxation times within a metabasin are short compared to an observation time scale. In this manner, equilibrium statistical mechanics is assumed within each metabasin, and the intermetabasin dynamics are computed using a reduced set of master equations. The number of metabasins depends upon both the temperature of the system and its derivative with respect to time. With this technique, the integration time step of the master equations is governed by the observation time scale rather than the fastest transition time between basins. We illustrate the technique using a simple model landscape with seven basins and show validation against direct Euler integration. Finally, we demonstrate the use of the technique for a realistic glass-forming system (viz., selenium) where direct Euler integration is not computationally feasible.

UR - http://www.scopus.com/inward/record.url?scp=34548150192&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548150192&partnerID=8YFLogxK

U2 - 10.1021/jp0731194

DO - 10.1021/jp0731194

M3 - Article

C2 - 17649986

AN - SCOPUS:34548150192

VL - 111

SP - 7957

EP - 7965

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

SN - 1089-5639

IS - 32

ER -