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

Journal Article · 25 June 2018 · Journal of Statistical Mechanics

DOI: https://doi.org/10.1088/1742-5468/aac915 · OSTI ID:1601181

Whitelam, Stephen ^[1]

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

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.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1601181

Alternate ID(s):: OSTI ID: 23006394

Journal Information:: Journal of Statistical Mechanics, Journal Name: Journal of Statistical Mechanics Journal Issue: 6 Vol. 2018; ISSN 1742-5468

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (50)

Phase separation and large deviations of lattice active matter Whitelam, Stephen; Klymko, Katherine; Mandal, Dibyendu The Journal of Chemical Physics, Vol. 148, Issue 15 https://doi.org/10.1063/1.5023403	journal	April 2018
Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles Garrahan, Juan P. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 7 https://doi.org/10.1088/1742-5468/2016/07/073208	journal	July 2016
Dynamical evolutions in non-Hermitian triple-well system with complex potential Guo, Liping; Du, Lei; Yin, Chuanhao arXiv https://doi.org/10.48550/arxiv.1803.03360	text	January 2018
Direct Evaluation of Large-Deviation Functions Giardinà, Cristian; Kurchan, Jorge; Peliti, Luca Physical Review Letters, Vol. 96, Issue 12 https://doi.org/10.1103/PhysRevLett.96.120603	journal	March 2006
Discrete-time thermodynamic uncertainty relation Proesmans, Karel; Van den Broeck, Christian EPL (Europhysics Letters), Vol. 119, Issue 2 https://doi.org/10.1209/0295-5075/119/20001	journal	July 2017
Dynamical Ensembles in Nonequilibrium Statistical Mechanics Gallavotti, G.; Cohen, E. G. D. arXiv https://doi.org/10.48550/arxiv.chao-dyn/9410007	text	January 1994
Effective interactions and large deviations in stochastic processes Jack, Robert L.; Sollich, Peter arXiv https://doi.org/10.48550/arxiv.1501.01154	text	January 2015
Universal bounds on current fluctuations Pietzonka, Patrick; Barato, Andre C.; Seifert, Udo Physical Review E, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevE.93.052145	journal	May 2016
Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling Torrie, G. M.; Valleau, J. P. Journal of Computational Physics, Vol. 23, Issue 2 https://doi.org/10.1016/0021-9991(77)90121-8	journal	February 1977
Fluctuation theorem for stochastic dynamics Kurchan, Jorge arXiv https://doi.org/10.48550/arxiv.cond-mat/9709304	text	January 1997
Nonequilibrium microcanonical and canonical ensembles and their equivalence Chetrite, Raphael; Touchette, Hugo arXiv https://doi.org/10.48550/arxiv.1306.4563	text	January 2013
Direct evaluation of large-deviation functions Giardina', Cristian; Kurchan, Jorge; Peliti, Luca arXiv https://doi.org/10.48550/arxiv.cond-mat/0511248	text	January 2005
Entropy Production along a Stochastic Trajectory and an Integral Fluctuation Theorem Seifert, Udo Physical Review Letters, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevLett.95.040602	journal	July 2005
Variational and optimal control representations of conditioned and driven processes Chetrite, Raphaël; Touchette, Hugo Journal of Statistical Mechanics: Theory and Experiment, Vol. 2015, Issue 12 https://doi.org/10.1088/1742-5468/2015/12/P12001	journal	December 2015
A general method for numerically simulating the stochastic time evolution of coupled chemical reactions Gillespie, Daniel T. Journal of Computational Physics, Vol. 22, Issue 4 https://doi.org/10.1016/0021-9991(76)90041-3	journal	December 1976
Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure Nemoto, Takahiro; Sasa, Shin-ichi Physical Review Letters, Vol. 112, Issue 9 https://doi.org/10.1103/PhysRevLett.112.090602	journal	March 2014
Weak measurements and quantum weak values for NOON states Rosales-Zárate, L.; Opanchuk, B.; Reid, M. D. Physical Review A, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevA.97.032123	journal	March 2018
Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T. Physical Review Letters, Vol. 120, Issue 21 https://doi.org/10.1103/physrevlett.120.210602	journal	May 2018
Phase separation and large deviations of lattice active matter Whitelam, Stephen; Klymko, Katherine; Mandal, Dibyendu arXiv https://doi.org/10.48550/arxiv.1709.03951	text	January 2017
A numerical approach to large deviations in continuous-time Lecomte, Vivien; Tailleur, Julien arXiv https://doi.org/10.48550/arxiv.cond-mat/0612561	text	January 2006
The large deviation function for entropy production: the optimal trajectory and the role of fluctuations Speck, Thomas; Engel, Andreas; Seifert, Udo Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 12 https://doi.org/10.1088/1742-5468/2012/12/P12001	journal	December 2012
Fluctuating observation time ensembles in the thermodynamics of trajectories Budini, Adrián A.; Turner, Robert M.; Garrahan, Juan P. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 3 https://doi.org/10.1088/1742-5468/2014/03/P03012	journal	March 2014
Dynamical Ensembles in Nonequilibrium Statistical Mechanics Gallavotti, G.; Cohen, E. G. D. Physical Review Letters, Vol. 74, Issue 14 https://doi.org/10.1103/PhysRevLett.74.2694	journal	April 1995
Bell inequalities violated using detectors of low efficiency Pal, Karoly F.; Vertesi, Tamas arXiv https://doi.org/10.48550/arxiv.1508.01494	text	January 2015
Proof of the finite-time thermodynamic uncertainty relation for steady-state currents Horowitz, Jordan M.; Gingrich, Todd R. Physical Review E, Vol. 96, Issue 2 https://doi.org/10.1103/PhysRevE.96.020103	journal	August 2017
Tightening the entropic uncertainty bound in the presence of quantum memory Adabi, F.; Salimi, S.; Haseli, S. Physical Review A, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevA.93.062123	journal	June 2016
A numerical approach to large deviations in continuous time Lecomte, Vivien; Tailleur, Julien Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 03 https://doi.org/10.1088/1742-5468/2007/03/P03004	journal	March 2007
Entropy production along a stochastic trajectory and an integral fluctuation theorem Seifert, Udo arXiv https://doi.org/10.48550/arxiv.cond-mat/0503686	text	January 2005
The large deviation approach to statistical mechanics Touchette, Hugo Physics Reports, Vol. 478, Issue 1-3 https://doi.org/10.1016/j.physrep.2009.05.002	journal	July 2009
Simulating Rare Events in Dynamical Processes Giardina, Cristian; Kurchan, Jorge; Lecomte, Vivien Journal of Statistical Physics, Vol. 145, Issue 4 https://doi.org/10.1007/s10955-011-0350-4	journal	September 2011
Effective interactions and large deviations in stochastic processes Jack, R. L.; Sollich, P. The European Physical Journal Special Topics, Vol. 224, Issue 12 https://doi.org/10.1140/epjst/e2015-02416-9	journal	June 2015
Path ensembles averages in systems driven far-from-equilibrium Crooks, Gavin E. arXiv https://doi.org/10.48550/arxiv.cond-mat/9908420	text	January 1999
First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories Garrahan, Juan P.; Jack, Robert L.; Lecomte, Vivien Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 7 https://doi.org/10.1088/1751-8113/42/7/075007	journal	January 2009
Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure Nemoto, Takahiro; Sasa, Shin-ichi arXiv https://doi.org/10.48550/arxiv.1309.7200	text	January 2013
First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories Garrahan, J. P.; Jack, R. L.; Lecomte, V. arXiv https://doi.org/10.48550/arxiv.0810.5298	text	January 2008
Tightening the entropic uncertainty bound in the presence of quantum memory Adabi, F.; Salimi, S.; Haseli, S. arXiv https://doi.org/10.48550/arxiv.1602.04296	text	January 2016
A Gallavotti–Cohen-Type Symmetry in the Large Deviation Functional for Stochastic Dynamics Lebowitz, Joel L.; Spohn, Herbert Journal of Statistical Physics, Vol. 95, Issue 1/2, p. 333-365 https://doi.org/10.1023/A:1004589714161	journal	January 1999
The large deviation approach to statistical mechanics Touchette, Hugo arXiv https://doi.org/10.48550/arxiv.0804.0327	text	January 2008
Scattering of accelerated wave packets Longhi, S.; Horsley, S. A. R.; Della Valle, G. Physical Review A, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevA.97.032122	journal	March 2018
Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states Maes, C.; Netočný, K. EPL (Europhysics Letters), Vol. 82, Issue 3 https://doi.org/10.1209/0295-5075/82/30003	journal	April 2008
Dissipation Bounds All Steady-State Current Fluctuations Gingrich, Todd R.; Horowitz, Jordan M.; Perunov, Nikolay Physical Review Letters, Vol. 116, Issue 12 https://doi.org/10.1103/PhysRevLett.116.120601	journal	March 2016
Fluctuation theorem for stochastic dynamics Kurchan, Jorge Journal of Physics A: Mathematical and General, Vol. 31, Issue 16 https://doi.org/10.1088/0305-4470/31/16/003	journal	April 1998
Multipartite nonlocality and random measurements de Rosier, Anna; Gruca, Jacek; Parisio, Fernando Physical Review A, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevA.96.012101	journal	July 2017
Path-ensemble averages in systems driven far from equilibrium Crooks, Gavin E. Physical Review E, Vol. 61, Issue 3 https://doi.org/10.1103/PhysRevE.61.2361	journal	March 2000
Dynamical evolutions in non-Hermitian triple-well systems with a complex potential Guo, Liping; Du, Lei; Yin, Chuanhao Physical Review A, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevA.97.032109	journal	March 2018
Nonequilibrium Microcanonical and Canonical Ensembles and Their Equivalence Chetrite, Raphaël; Touchette, Hugo Physical Review Letters, Vol. 111, Issue 12 https://doi.org/10.1103/PhysRevLett.111.120601	journal	September 2013
Dissipation bounds all steady-state current fluctuations Gingrich, Todd R.; Horowitz, Jordan M.; Perunov, Nikolay arXiv https://doi.org/10.48550/arxiv.1512.02212	text	January 2015
Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents Horowitz, Jordan M.; Gingrich, Todd R. arXiv https://doi.org/10.48550/arxiv.1707.03805	text	January 2017
Bell inequalities violated using detectors of low efficiency Pál, Károly F.; Vértesi, Tamás Physical Review A, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevA.92.052104	journal	November 2015
Large Deviations Techniques and Applications Dembo, Amir; Zeitouni, Ofer https://doi.org/10.1007/978-3-642-03311-7	book	January 2010

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Direct evaluation of dynamical large-deviation rate functions using a variational ansatz Jacobson, Daniel; Whitelam, Stephen Physical Review E, Vol. 100, Issue 5 https://doi.org/10.1103/physreve.100.052139	journal	November 2019

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