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

Daniel Jacobson and Stephen Whitelam
Phys. Rev. E 100, 052139 – Published 25 November 2019

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 ansätze yield bounds that are tighter than bounds obtained from Level 2.5 of large deviations via approximations that involve uniform scalings of rates. 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.

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  • Received 1 May 2019
  • Revised 18 September 2019

DOI:https://doi.org/10.1103/PhysRevE.100.052139

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Daniel Jacobson1,* and Stephen Whitelam2,†

  • 1Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
  • 2Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA

  • *Daniel.Jacobson@caltech.edu
  • swhitelam@lbl.gov

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Issue

Vol. 100, Iss. 5 — November 2019

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