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Direct evaluation of dynamical large-deviation rate functions using a variational ansatz

Jacobson, Daniel and Whitelam, Stephen (2019) Direct evaluation of dynamical large-deviation rate functions using a variational ansatz. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190513-103602196

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Abstract

We describe a simple form of importance sampling designed to bound and compute large-deviation rate functions for time-extensive dynamical observables in continuous-time Markov chains. We start with a model, defined by a set of rates, and a time-extensive 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 large-deviation 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 ansatze yield bounds that are tighter than bounds obtained from Level 2.5 of large deviations via approximations that homogenize connections between states. 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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1903.06098arXivDiscussion Paper
Additional Information:We thank Hugo Touchette, Tom Ouldridge, and Juan Garrahan for discussions and comments on the manuscript, and thank Juan Garrahan, Todd Gingrich, and Mari Carmen Ba~nuls for providing data from Refs. [54], [16], and [80], respectively. This work was performed as part of a user project at the Molecular Foundry, Lawrence Berkeley National Laboratory, supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. DJ acknowledges support from the Department of Energy Computational Science Graduate Fellowship.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC02-05CH11231
Record Number:CaltechAUTHORS:20190513-103602196
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190513-103602196
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95429
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 May 2019 17:40
Last Modified:13 May 2019 17:40

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