Direct evaluation of dynamical largedeviation rate functions using a variational ansatz
Abstract
We describe a simple form of importance sampling designed to bound and compute largedeviation rate functions for timeextensive dynamical observables in continuoustime Markov chains. We start with a model, defined by a set of rates, and a timeextensive dynamical observable. We construct a reference model, a variational ansatz for the behavior of the original model conditioned on atypical values of the observable. Direct simulation of the reference model provides an upper bound on the largedeviation rate function associated with the original model, an estimate of the tightness of the bound, and, if the ansatz is chosen well, the exact rate function. The exact rare behavior of the original model does not need to be known in advance. We use this method to calculate rate functions for currents and counting observables in a set of network and lattice models taken from the literature. Straightforward ansätze yield bounds that are tighter than bounds obtained from Level 2.5 of large deviations via approximations that involve uniform scalings of rates. Here, we show how to correct these bounds in order to recover the rate functions exactly. Our approach is complementary to more specialized methods and offers a physically transparent framework for approximating and calculatingmore »
 Authors:

 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES)
 OSTI Identifier:
 1601210
 Grant/Contract Number:
 AC0205CH11231
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. E
 Additional Journal Information:
 Journal Volume: 100; Journal Issue: 5; Journal ID: ISSN 24700045
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Jacobson, Daniel, and Whitelam, Stephen. Direct evaluation of dynamical largedeviation rate functions using a variational ansatz. United States: N. p., 2019.
Web. doi:10.1103/physreve.100.052139.
Jacobson, Daniel, & Whitelam, Stephen. Direct evaluation of dynamical largedeviation rate functions using a variational ansatz. United States. https://doi.org/10.1103/physreve.100.052139
Jacobson, Daniel, and Whitelam, Stephen. Mon .
"Direct evaluation of dynamical largedeviation rate functions using a variational ansatz". United States. https://doi.org/10.1103/physreve.100.052139. https://www.osti.gov/servlets/purl/1601210.
@article{osti_1601210,
title = {Direct evaluation of dynamical largedeviation rate functions using a variational ansatz},
author = {Jacobson, Daniel and Whitelam, Stephen},
abstractNote = {We describe a simple form of importance sampling designed to bound and compute largedeviation rate functions for timeextensive dynamical observables in continuoustime Markov chains. We start with a model, defined by a set of rates, and a timeextensive dynamical observable. We construct a reference model, a variational ansatz for the behavior of the original model conditioned on atypical values of the observable. Direct simulation of the reference model provides an upper bound on the largedeviation rate function associated with the original model, an estimate of the tightness of the bound, and, if the ansatz is chosen well, the exact rate function. The exact rare behavior of the original model does not need to be known in advance. We use this method to calculate rate functions for currents and counting observables in a set of network and lattice models taken from the literature. Straightforward ansätze yield bounds that are tighter than bounds obtained from Level 2.5 of large deviations via approximations that involve uniform scalings of rates. Here, we show how to correct these bounds in order to recover the rate functions exactly. Our approach is complementary to more specialized methods and offers a physically transparent framework for approximating and calculating the likelihood of dynamical large deviations.},
doi = {10.1103/physreve.100.052139},
journal = {Physical Review. E},
number = 5,
volume = 100,
place = {United States},
year = {2019},
month = {11}
}
Web of Science
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