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Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization

Ray, Ushnish and Chan, Garnet Kin-Lic (2020) Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization. Journal of Chemical Physics, 152 (10). Art. No. 104107. ISSN 0021-9606. doi:10.1063/1.5143144.

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We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study the interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D weakly asymmetric simple exclusion process. We show that with modest resources, we can capture the features of the susceptibility in large systems that mark the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper ItemCANSS
Ray, Ushnish0000-0002-1850-4691
Chan, Garnet Kin-Lic0000-0001-8009-6038
Alternate Title:Constructing Auxiliary Dynamics for Nonequilibrium Stationary States with Variational Monte-Carlo
Additional Information:© 2020 Published under license by AIP Publishing. Submitted: 19 December 2019; Accepted: 24 February 2020; Published Online: 12 March 2020. The authors would like to thank Rob Jack, Vivien Lecomte, Juan P. Garrahan, and David Limmer for fruitful and engaging discussions. U.R. was supported by the Simons Collaboration on the Many-Electron Problem and the California Institute of Technology. G.K.-L.C. is a Simons Investigator in Theoretical Physics and was supported by the California Institute of Technology and the U.S. Department of Energy, Office of Science, via Grant No. DE-SC0018140. These calculations were performed with CANSS, available at
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0018140
Issue or Number:10
Record Number:CaltechAUTHORS:20200122-091951274
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Official Citation:Constructing auxiliary dynamics for nonequilibrium stationary states by variance minimization. Ushnish Ray and Garnet Kin-Lic Chan. The Journal of Chemical Physics 152:10; doi: 10.1063/1.5143144
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100831
Deposited By: Tony Diaz
Deposited On:22 Jan 2020 17:30
Last Modified:16 Nov 2021 17:57

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