Multi-point nonequilibrium umbrella sampling and associated fluctuation relations

Whitelam, Stephen

doi:10.1088/1742-5468/aac915

Title: Multi-point nonequilibrium umbrella sampling and associated fluctuation relations

Abstract

We describe a simple method of umbrella trajectory sampling for Markov chains. The method allows the estimation of large-deviation rate functions, for path-extensive dynamic observables, for an arbitrary number of models within a certain family. The general relationship between probability distributions of dynamic observables of members of this family is an extended fluctuation relation. When the dynamic observable is chosen to be entropy production, members of this family include the forward Markov chain and its time reverse, whose probability distributions are related by the expected simple fluctuation relation.

Authors:

Whitelam, Stephen ^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Publication Date:: 2018-06-26

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1601181

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Statistical Mechanics

Additional Journal Information:: Journal Volume: 2018; Journal Issue: 6; Journal ID: ISSN 1742-5468

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Whitelam, Stephen. Multi-point nonequilibrium umbrella sampling and associated fluctuation relations.  United States: N. p., 2018. 
        Web.  doi:10.1088/1742-5468/aac915.

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                    Whitelam, Stephen. Multi-point nonequilibrium umbrella sampling and associated fluctuation relations.  United States.  doi:https://doi.org/10.1088/1742-5468/aac915

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                    Whitelam, Stephen. Tue .  
        "Multi-point nonequilibrium umbrella sampling and associated fluctuation relations".  United States.  doi:https://doi.org/10.1088/1742-5468/aac915.  https://www.osti.gov/servlets/purl/1601181.

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@article{osti_1601181,

  title        = {Multi-point nonequilibrium umbrella sampling and associated fluctuation relations},

  author       = {Whitelam, Stephen},

  abstractNote = {We describe a simple method of umbrella trajectory sampling for Markov chains. The method allows the estimation of large-deviation rate functions, for path-extensive dynamic observables, for an arbitrary number of models within a certain family. The general relationship between probability distributions of dynamic observables of members of this family is an extended fluctuation relation. When the dynamic observable is chosen to be entropy production, members of this family include the forward Markov chain and its time reverse, whose probability distributions are related by the expected simple fluctuation relation.},

  doi          = {10.1088/1742-5468/aac915},

  journal      = {Journal of Statistical Mechanics},

  number       = 6,

  volume       = 2018,

  place        = {United States},

  year         = {2018},

  month        = {6}

}

Copy to clipboard

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DOI: https://doi.org/10.1088/1742-5468/aac915

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Works referenced in this record:

Effective interactions and large deviations in stochastic processes
journal, June 2015

Jack, R. L.; Sollich, P.
The European Physical Journal Special Topics, Vol. 224, Issue 12
DOI: 10.1140/epjst/e2015-02416-9

Dynamical Ensembles in Nonequilibrium Statistical Mechanics
journal, April 1995

Gallavotti, G.; Cohen, E. G. D.
Physical Review Letters, Vol. 74, Issue 14
DOI: 10.1103/PhysRevLett.74.2694

Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling
journal, February 1977

Torrie, G. M.; Valleau, J. P.
Journal of Computational Physics, Vol. 23, Issue 2
DOI: 10.1016/0021-9991(77)90121-8

Phase separation and large deviations of lattice active matter
journal, April 2018

Whitelam, Stephen; Klymko, Katherine; Mandal, Dibyendu
The Journal of Chemical Physics, Vol. 148, Issue 15
DOI: 10.1063/1.5023403

Fluctuation theorem for stochastic dynamics
journal, April 1998

Kurchan, Jorge
Journal of Physics A: Mathematical and General, Vol. 31, Issue 16
DOI: 10.1088/0305-4470/31/16/003

Proof of the finite-time thermodynamic uncertainty relation for steady-state currents
journal, August 2017

Horowitz, Jordan M.; Gingrich, Todd R.
Physical Review E, Vol. 96, Issue 2
DOI: 10.1103/PhysRevE.96.020103

Entropy Production along a Stochastic Trajectory and an Integral Fluctuation Theorem
journal, July 2005

Seifert, Udo
Physical Review Letters, Vol. 95, Issue 4
DOI: 10.1103/PhysRevLett.95.040602

Bell inequalities violated using detectors of low efficiency
journal, November 2015

Pál, Károly F.; Vértesi, Tamás
Physical Review A, Vol. 92, Issue 5
DOI: 10.1103/PhysRevA.92.052104

Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure
journal, March 2014

Nemoto, Takahiro; Sasa, Shin-ichi
Physical Review Letters, Vol. 112, Issue 9
DOI: 10.1103/PhysRevLett.112.090602

Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles
journal, July 2016

Garrahan, Juan P.
Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 7
DOI: 10.1088/1742-5468/2016/07/073208

The large deviation function for entropy production: the optimal trajectory and the role of fluctuations
journal, December 2012

Speck, Thomas; Engel, Andreas; Seifert, Udo
Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 12
DOI: 10.1088/1742-5468/2012/12/P12001

Universal bounds on current fluctuations
journal, May 2016

Pietzonka, Patrick; Barato, Andre C.; Seifert, Udo
Physical Review E, Vol. 93, Issue 5
DOI: 10.1103/PhysRevE.93.052145

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

Gingrich, Todd R.; Horowitz, Jordan M.; Perunov, Nikolay
Physical Review Letters, Vol. 116, Issue 12
DOI: 10.1103/PhysRevLett.116.120601

Multipartite nonlocality and random measurements
journal, July 2017

de Rosier, Anna; Gruca, Jacek; Parisio, Fernando
Physical Review A, Vol. 96, Issue 1
DOI: 10.1103/PhysRevA.96.012101

Tightening the entropic uncertainty bound in the presence of quantum memory
journal, June 2016

Adabi, F.; Salimi, S.; Haseli, S.
Physical Review A, Vol. 93, Issue 6
DOI: 10.1103/PhysRevA.93.062123

Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics
journal, May 2018

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.
Physical Review Letters, Vol. 120, Issue 21
DOI: 10.1103/physrevlett.120.210602

Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
journal, April 2008

Maes, C.; Netočný, K.
EPL (Europhysics Letters), Vol. 82, Issue 3
DOI: 10.1209/0295-5075/82/30003

Path-ensemble averages in systems driven far from equilibrium
journal, March 2000

Crooks, Gavin E.
Physical Review E, Vol. 61, Issue 3
DOI: 10.1103/PhysRevE.61.2361

The large deviation approach to statistical mechanics
journal, July 2009

Touchette, Hugo
Physics Reports, Vol. 478, Issue 1-3
DOI: 10.1016/j.physrep.2009.05.002

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

Giardinà, Cristian; Kurchan, Jorge; Peliti, Luca
Physical Review Letters, Vol. 96, Issue 12
DOI: 10.1103/PhysRevLett.96.120603

Nonequilibrium Microcanonical and Canonical Ensembles and Their Equivalence
journal, September 2013

Chetrite, Raphaël; Touchette, Hugo
Physical Review Letters, Vol. 111, Issue 12
DOI: 10.1103/PhysRevLett.111.120601

Dynamical evolutions in non-Hermitian triple-well systems with a complex potential
journal, March 2018

Guo, Liping; Du, Lei; Yin, Chuanhao
Physical Review A, Vol. 97, Issue 3
DOI: 10.1103/PhysRevA.97.032109

First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
journal, January 2009

Garrahan, Juan P.; Jack, Robert L.; Lecomte, Vivien
Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 7
DOI: 10.1088/1751-8113/42/7/075007

Discrete-time thermodynamic uncertainty relation
journal, July 2017

Proesmans, Karel; Van den Broeck, Christian
EPL (Europhysics Letters), Vol. 119, Issue 2
DOI: 10.1209/0295-5075/119/20001

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
journal, December 1976

Gillespie, Daniel T.
Journal of Computational Physics, Vol. 22, Issue 4
DOI: 10.1016/0021-9991(76)90041-3

A numerical approach to large deviations in continuous time
journal, March 2007

Lecomte, Vivien; Tailleur, Julien
Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 03
DOI: 10.1088/1742-5468/2007/03/P03004

Variational and optimal control representations of conditioned and driven processes
journal, December 2015

Chetrite, Raphaël; Touchette, Hugo
Journal of Statistical Mechanics: Theory and Experiment, Vol. 2015, Issue 12
DOI: 10.1088/1742-5468/2015/12/P12001

Weak measurements and quantum weak values for NOON states
journal, March 2018

Rosales-Zárate, L.; Opanchuk, B.; Reid, M. D.
Physical Review A, Vol. 97, Issue 3
DOI: 10.1103/PhysRevA.97.032123

Scattering of accelerated wave packets
journal, March 2018

Longhi, S.; Horsley, S. A. R.; Della Valle, G.
Physical Review A, Vol. 97, Issue 3
DOI: 10.1103/PhysRevA.97.032122

Fluctuating observation time ensembles in the thermodynamics of trajectories
journal, March 2014

Budini, Adrián A.; Turner, Robert M.; Garrahan, Juan P.
Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 3
DOI: 10.1088/1742-5468/2014/03/P03012

Works referencing / citing this record:

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

Jacobson, Daniel; Whitelam, Stephen
Physical Review E, Vol. 100, Issue 5
DOI: 10.1103/physreve.100.052139

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Similar Records

Title: Multi-point nonequilibrium umbrella sampling and associated fluctuation relations

Abstract

Citation Formats

Effective interactions and large deviations in stochastic processes journal, June 2015

Dynamical Ensembles in Nonequilibrium Statistical Mechanics journal, April 1995

Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling journal, February 1977

Phase separation and large deviations of lattice active matter journal, April 2018

Fluctuation theorem for stochastic dynamics journal, April 1998

Proof of the finite-time thermodynamic uncertainty relation for steady-state currents journal, August 2017

Entropy Production along a Stochastic Trajectory and an Integral Fluctuation Theorem journal, July 2005

Bell inequalities violated using detectors of low efficiency journal, November 2015

Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure journal, March 2014

Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles journal, July 2016

The large deviation function for entropy production: the optimal trajectory and the role of fluctuations journal, December 2012

Universal bounds on current fluctuations journal, May 2016

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

Multipartite nonlocality and random measurements journal, July 2017

Tightening the entropic uncertainty bound in the presence of quantum memory journal, June 2016

Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics journal, May 2018

Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states journal, April 2008

Path-ensemble averages in systems driven far from equilibrium journal, March 2000

The large deviation approach to statistical mechanics journal, July 2009

Simulating Rare Events in Dynamical Processes journal, September 2011

Direct Evaluation of Large-Deviation Functions journal, March 2006

Nonequilibrium Microcanonical and Canonical Ensembles and Their Equivalence journal, September 2013

Dynamical evolutions in non-Hermitian triple-well systems with a complex potential journal, March 2018

First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories journal, January 2009

Discrete-time thermodynamic uncertainty relation journal, July 2017

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions journal, December 1976

A numerical approach to large deviations in continuous time journal, March 2007

Variational and optimal control representations of conditioned and driven processes journal, December 2015

Weak measurements and quantum weak values for NOON states journal, March 2018

Scattering of accelerated wave packets journal, March 2018

Fluctuating observation time ensembles in the thermodynamics of trajectories journal, March 2014

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

Effective interactions and large deviations in stochastic processes
journal, June 2015

Dynamical Ensembles in Nonequilibrium Statistical Mechanics
journal, April 1995

Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling
journal, February 1977

Phase separation and large deviations of lattice active matter
journal, April 2018

Fluctuation theorem for stochastic dynamics
journal, April 1998

Proof of the finite-time thermodynamic uncertainty relation for steady-state currents
journal, August 2017

Entropy Production along a Stochastic Trajectory and an Integral Fluctuation Theorem
journal, July 2005

Bell inequalities violated using detectors of low efficiency
journal, November 2015

Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure
journal, March 2014

Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles
journal, July 2016

The large deviation function for entropy production: the optimal trajectory and the role of fluctuations
journal, December 2012

Universal bounds on current fluctuations
journal, May 2016

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

Multipartite nonlocality and random measurements
journal, July 2017

Tightening the entropic uncertainty bound in the presence of quantum memory
journal, June 2016

Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics
journal, May 2018

Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
journal, April 2008

Path-ensemble averages in systems driven far from equilibrium
journal, March 2000

The large deviation approach to statistical mechanics
journal, July 2009

Simulating Rare Events in Dynamical Processes
journal, September 2011

Direct Evaluation of Large-Deviation Functions
journal, March 2006

Nonequilibrium Microcanonical and Canonical Ensembles and Their Equivalence
journal, September 2013

Dynamical evolutions in non-Hermitian triple-well systems with a complex potential
journal, March 2018

First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
journal, January 2009

Discrete-time thermodynamic uncertainty relation
journal, July 2017

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
journal, December 1976

A numerical approach to large deviations in continuous time
journal, March 2007

Variational and optimal control representations of conditioned and driven processes
journal, December 2015

Weak measurements and quantum weak values for NOON states
journal, March 2018

Scattering of accelerated wave packets
journal, March 2018

Fluctuating observation time ensembles in the thermodynamics of trajectories
journal, March 2014

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