# 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:

- 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:

- 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.
```

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

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

```
@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 = {2018},

month = {5}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

*= 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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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*