Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.

doi:10.1103/PhysRevLett.120.210602

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:

Ray, Ushnish ^[1]; Chan, Garnet Kin-Lic ^[1]; Limmer, David T. ^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Division of Chemistry and Chemical Engineering
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:: Tue May 22 00:00:00 EDT 2018

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.

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                    Ray, Ushnish, Chan, Garnet Kin-Lic, & Limmer, David T. Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics.  United States.  https://doi.org/10.1103/PhysRevLett.120.210602

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                    Ray, Ushnish, Chan, Garnet Kin-Lic, and Limmer, David T. Tue .  
"Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics".  United States.  https://doi.org/10.1103/PhysRevLett.120.210602.  https://www.osti.gov/servlets/purl/1461153.

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@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         = {Tue May 22 00:00:00 EDT 2018},

  month        = {Tue May 22 00:00:00 EDT 2018}

}

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https://doi.org/10.1103/PhysRevLett.120.210602

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Cited by: 45 works

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Figures / Tables:

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 »

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

Abstract

Citation Formats

Figures / Tables:

Genealogical particle analysis of rare events journal, November 2005

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

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

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

Fluctuation theorem for stochastic dynamics journal, April 1998

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

Quantum Monte Carlo simulations of solids journal, January 2001

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

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

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

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

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

Fluctuation theorems for stochastic dynamics journal, July 2007

Classical potential theory and its probabilistic counterpart: Doob JL: A series of comprehensive Studies in Mathematics, Bd 262, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo 1984, 846 S, DM 168 journal, December 1986

The large deviation approach to statistical mechanics text, January 2008

A multiple replica approach to simulate reactive trajectories text, January 2010

Thermodynamic uncertainty relation for biomolecular processes text, January 2015

Dissipation bounds all steady-state current fluctuations text, January 2015

Population dynamics method with a multi-canonical feedback control text, January 2016

Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model text, January 2016

Rare behavior of growth processes via umbrella sampling of trajectories text, January 2017

Importance sampling large deviations in nonequilibrium steady states. I text, January 2017

Dynamical Ensembles in Nonequilibrium Statistical Mechanics text, January 1994

Equality connecting energy dissipation with violation of fluctuation-response relation text, January 2005

Direct evaluation of large-deviation functions text, January 2005

Fluctuation theorems for stochastic dynamics text, January 2007

Fluctuation theorem for stochastic dynamics text, January 1997

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

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

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

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

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

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

Large deviations and optimal control forces for hard particles in one dimension text, January 2019

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

Large deviations in models of growing clusters with symmetry-breaking transitions. text, January 2019

Current fluctuations of interacting active Brownian particles text, January 2018

How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions text, January 2018

Large-deviation theory for a Brownian particle on a ring: a WKB approach text, January 2018

Nonlinear transport coefficients from large deviation functions text, January 2018

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

Large deviations conditioned on large deviations II: Fluctuating hydrodynamics text, January 2019

Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations text, January 2019

Genealogical particle analysis of rare events
journal, November 2005

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

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

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

Fluctuation theorem for stochastic dynamics
journal, April 1998

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

Quantum Monte Carlo simulations of solids
journal, January 2001

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

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

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

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

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

Fluctuation theorems for stochastic dynamics
journal, July 2007

Classical potential theory and its probabilistic counterpart: Doob JL: A series of comprehensive Studies in Mathematics, Bd 262, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo 1984, 846 S, DM 168
journal, December 1986

The large deviation approach to statistical mechanics
text, January 2008

A multiple replica approach to simulate reactive trajectories
text, January 2010

Thermodynamic uncertainty relation for biomolecular processes
text, January 2015

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text, January 2015

Population dynamics method with a multi-canonical feedback control
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Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
text, January 2016

Rare behavior of growth processes via umbrella sampling of trajectories
text, January 2017

Importance sampling large deviations in nonequilibrium steady states. I
text, January 2017

Dynamical Ensembles in Nonequilibrium Statistical Mechanics
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Direct evaluation of large-deviation functions
text, January 2005

Fluctuation theorems for stochastic dynamics
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Fluctuation theorem for stochastic dynamics
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journal, September 2019

Perspective: Computational chemistry software and its advancement as illustrated through three grand challenge cases for molecular science
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journal, July 2019

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

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

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

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit
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Large-deviation theory for a Brownian particle on a ring: a WKB approach
journal, February 2019

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journal, December 2019

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

Large deviations and optimal control forces for hard particles in one dimension
text, January 2019

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

Large deviations in models of growing clusters with symmetry-breaking transitions.
text, January 2019

Current fluctuations of interacting active Brownian particles
text, January 2018

How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions
text, January 2018

Large-deviation theory for a Brownian particle on a ring: a WKB approach
text, January 2018

Nonlinear transport coefficients from large deviation functions
text, January 2018

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

Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
text, January 2019

Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations
text, January 2019