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Title: Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics

Abstract

We describe a framework to reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance samples the trajectories that most contribute to the large deviation function, mitigating the exponential complexity of such calculations. Here, we illustrate the method by studying driven diffusion and interacting lattice models in one and two spatial dimensions. Finally, our work offers an avenue to calculate large deviation functions for high dimensional systems driven far from equilibrium.

Authors:
 [1];  [1];  [2]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Division of Chemistry and Chemical Engineering
  2. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; Kavli Energy NanoScience Inst., Berkeley CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Science Division
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1461153
Alternate Identifier(s):
OSTI ID: 1438273
Grant/Contract Number:  
AC02-05CH11231; SC0018140
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 120; Journal Issue: 21; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Ray, Ushnish, Chan, Garnet Kin-Lic, and Limmer, David T. Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics. United States: N. p., 2018. Web. doi:10.1103/PhysRevLett.120.210602.
Ray, Ushnish, Chan, Garnet Kin-Lic, & Limmer, David T. Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics. United States. doi:https://doi.org/10.1103/PhysRevLett.120.210602
Ray, Ushnish, Chan, Garnet Kin-Lic, and Limmer, David T. Tue . "Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics". United States. doi:https://doi.org/10.1103/PhysRevLett.120.210602. https://www.osti.gov/servlets/purl/1461153.
@article{osti_1461153,
title = {Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics},
author = {Ray, Ushnish and Chan, Garnet Kin-Lic and Limmer, David T.},
abstractNote = {We describe a framework to reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance samples the trajectories that most contribute to the large deviation function, mitigating the exponential complexity of such calculations. Here, we illustrate the method by studying driven diffusion and interacting lattice models in one and two spatial dimensions. Finally, our work offers an avenue to calculate large deviation functions for high dimensional systems driven far from equilibrium.},
doi = {10.1103/PhysRevLett.120.210602},
journal = {Physical Review Letters},
number = 21,
volume = 120,
place = {United States},
year = {2018},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 9 works
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Figures / Tables:

FIG. 1 FIG. 1: Large deviation function for the entropy production of a driven brownian particle on a periodic potential with $v$o = 2, $f$ = 12.5. The main figure shows the functions computed with exact diagonalization (red) and DMC (black). The inset shows the fraction of correlated walkers without GDF (blue),more » or with GDF from an instanton approximation to the auxiliary process (red) or the exact auxiliary process (black).« less

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Works referenced in this record:

Genealogical particle analysis of rare events
journal, November 2005


Large deviations of the current for driven periodic diffusions
journal, September 2016


Stochastic thermodynamics, fluctuation theorems and molecular machines
journal, November 2012


Dynamical Ensembles in Nonequilibrium Statistical Mechanics
journal, April 1995


Projector quantum Monte Carlo with matrix product states
journal, July 2014


Equality Connecting Energy Dissipation with a Violation of the Fluctuation-Response Relation
journal, September 2005


Nonequilibrium steady states of matrix-product form: a solver's guide
journal, October 2007


Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
journal, March 2017


Large deviation function for entropy production in driven one-dimensional systems
journal, July 2008


Fluctuation theorem for stochastic dynamics
journal, April 1998


Importance sampling large deviations in nonequilibrium steady states. I
journal, March 2018

  • Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.
  • The Journal of Chemical Physics, Vol. 148, Issue 12
  • DOI: 10.1063/1.5003151

Thermodynamic Uncertainty Relation for Biomolecular Processes
journal, April 2015


Quantum Monte Carlo simulations of solids
journal, January 2001


Fluctuations and Response of Nonequilibrium States
journal, July 2009


Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences
journal, September 1999


Order and Symmetry Breaking in the Fluctuations of Driven Systems
journal, August 2017


T RANSITION P ATH S AMPLING : Throwing Ropes Over Rough Mountain Passes, in the Dark
journal, October 2002


Rare behavior of growth processes via umbrella sampling of trajectories
journal, March 2018


Large Fluctuations in Driven Dissipative Media
journal, September 2011


Dissipation Bounds All Steady-State Current Fluctuations
journal, March 2016


Kinetic Ising Model of the Glass Transition
journal, September 1984


Population-dynamics method with a multicanonical feedback control
journal, June 2016


Ground State of the Electron Gas by a Stochastic Method
journal, August 1980


The large deviation approach to statistical mechanics
journal, July 2009


Simulating Rare Events in Dynamical Processes
journal, September 2011

  • Giardina, Cristian; Kurchan, Jorge; Lecomte, Vivien
  • Journal of Statistical Physics, Vol. 145, Issue 4
  • DOI: 10.1007/s10955-011-0350-4

Direct Evaluation of Large-Deviation Functions
journal, March 2006


A multiple replica approach to simulate reactive trajectories
journal, February 2011

  • Cérou, Frédéric; Guyader, Arnaud; Lelièvre, Tony
  • The Journal of Chemical Physics, Vol. 134, Issue 5
  • DOI: 10.1063/1.3518708

Go with the winners: a general Monte Carlo strategy
journal, August 2002


Fluctuation–dissipation: Response theory in statistical physics
journal, June 2008


Large Deviations and Ensembles of Trajectories in Stochastic Models
journal, January 2010

  • Jack, Robert L.; Sollich, Peter
  • Progress of Theoretical Physics Supplement, Vol. 184
  • DOI: 10.1143/PTPS.184.304

Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state
journal, May 2006


Fluctuation theorems for stochastic dynamics
journal, July 2007


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    • Krylov, Anna; Windus, Theresa L.; Barnes, Taylor
    • The Journal of Chemical Physics, Vol. 149, Issue 18
    • DOI: 10.1063/1.5052551

    Sampling rare events across dynamical phase transitions
    journal, August 2019

    • Pérez-Espigares, Carlos; Hurtado, Pablo I.
    • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 29, Issue 8
    • DOI: 10.1063/1.5091669

    Nonlinear transport coefficients from large deviation functions
    journal, July 2019

    • Gao, Chloe Ya; Limmer, David T.
    • The Journal of Chemical Physics, Vol. 151, Issue 1
    • DOI: 10.1063/1.5110507

    Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations
    journal, December 2019

    • Das, Avishek; Limmer, David T.
    • The Journal of Chemical Physics, Vol. 151, Issue 24
    • DOI: 10.1063/1.5128956

    Dissipation controls transport and phase transitions in active fluids: mobility, diffusion and biased ensembles
    journal, January 2020

    • Fodor, Étienne; Nemoto, Takahiro; Vaikuntanathan, Suriyanarayanan
    • New Journal of Physics, Vol. 22, Issue 1
    • DOI: 10.1088/1367-2630/ab6353

    Multi-point nonequilibrium umbrella sampling and associated fluctuation relations
    journal, June 2018

    • Whitelam, Stephen
    • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, Issue 6
    • DOI: 10.1088/1742-5468/aac915

    Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit
    journal, January 2019

    • Tizón-Escamilla, Nicolás; Lecomte, Vivien; Bertin, Eric
    • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 1
    • DOI: 10.1088/1742-5468/aaeda3

    Large-deviation theory for a Brownian particle on a ring: a WKB approach
    journal, February 2019

    • Proesmans, Karel; Derrida, Bernard
    • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 2
    • DOI: 10.1088/1742-5468/aafa7e

    Large deviations and optimal control forces for hard particles in one dimension
    journal, December 2019

    • Dolezal, Jakub; Jack, Robert L.
    • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 12
    • DOI: 10.1088/1742-5468/ab4801

    Large deviations in models of growing clusters with symmetry-breaking transitions
    journal, July 2019


    Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
    journal, August 2019


    Direct evaluation of dynamical large-deviation rate functions using a variational ansatz
    journal, November 2019


    Current fluctuations of interacting active Brownian particles
    journal, December 2018


    Optimizing active work: Dynamical phase transitions, collective motion, and jamming
    journal, February 2019


    How Dissipation Constrains Fluctuations in Nonequilibrium Liquids: Diffusion, Structure, and Biased Interactions
    journal, November 2019


      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.