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

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Works referenced in this record:

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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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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

The large deviation approach to statistical mechanics text, January 2008

First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories text, January 2008

Nonequilibrium microcanonical and canonical ensembles and their equivalence text, January 2013

Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure text, January 2013

Effective interactions and large deviations in stochastic processes text, January 2015

Bell inequalities violated using detectors of low efficiency text, January 2015

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

Tightening the entropic uncertainty bound in the presence of quantum memory text, January 2016

Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents text, January 2017

Phase separation and large deviations of lattice active matter text, January 2017

Dynamical evolutions in non-Hermitian triple-well system with complex potential text, January 2018

Dynamical Ensembles in Nonequilibrium Statistical Mechanics text, January 1994

Entropy production along a stochastic trajectory and an integral fluctuation theorem text, January 2005

Direct evaluation of large-deviation functions text, January 2005

A numerical approach to large deviations in continuous-time text, January 2006

Fluctuation theorem for stochastic dynamics text, January 1997

Path ensembles averages in systems driven far-from-equilibrium text, January 1999

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

The large deviation approach to statistical mechanics
text, January 2008

First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
text, January 2008

Nonequilibrium microcanonical and canonical ensembles and their equivalence
text, January 2013

Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure
text, January 2013

Effective interactions and large deviations in stochastic processes
text, January 2015

Bell inequalities violated using detectors of low efficiency
text, January 2015

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

Tightening the entropic uncertainty bound in the presence of quantum memory
text, January 2016

Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
text, January 2017

Phase separation and large deviations of lattice active matter
text, January 2017

Dynamical evolutions in non-Hermitian triple-well system with complex potential
text, January 2018

Dynamical Ensembles in Nonequilibrium Statistical Mechanics
text, January 1994

Entropy production along a stochastic trajectory and an integral fluctuation theorem
text, January 2005

Direct evaluation of large-deviation functions
text, January 2005

A numerical approach to large deviations in continuous-time
text, January 2006

Fluctuation theorem for stochastic dynamics
text, January 1997

Path ensembles averages in systems driven far-from-equilibrium
text, January 1999

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