# Tests for, origins of, and corrections to non-Gaussian statistics. The dipole-flip model

## Abstract

Linear response approximations are central to our understanding and simulations of nonequilibrium statistical mechanics. Despite the success of these approaches in predicting nonequilibrium dynamics, open questions remain. Laird and Thompson [J. Chem. Phys. 126, 211104 (2007)] previously formalized, in the context of solvation dynamics, the connection between the static linear-response approximation and the assumption of Gaussian statistics. The Gaussian statistics perspective is useful in understanding why linear response approximations are still accurate for perturbations much larger than thermal energies. In this study, we use this approach to address three outstanding issues in the context of the “dipole-flip” model, which is known to exhibit nonlinear response. First, we demonstrate how non-Gaussian statistics can be predicted from purely equilibrium molecular dynamics (MD) simulations (i.e., without resort to a full nonequilibrium MD as is the current practice). Second, we show that the Gaussian statistics approximation may also be used to identify the physical origins of nonlinear response residing in a small number of coordinates. Third, we explore an approach for correcting the Gaussian statistics approximation for nonlinear response effects using the same equilibrium simulation. Finally, the results are discussed in the context of several other examples of nonlinear responses throughout the literature.

- Authors:

- Univ. of Kansas, Lawrence, KS (United States). Dept. of Chemistry

- Publication Date:

- Research Org.:
- Univ. of Kansas, Lawrence, KS (United States)

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

- OSTI Identifier:
- 1465977

- Alternate Identifier(s):
- OSTI ID: 1361826

- Grant/Contract Number:
- FG02-05ER15708

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 146; Journal Issue: 15; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; statistical analysis; hydrogen bonding; fluorescence; excited states; solvents; correlation functions; band gap; ground states; molecular dynamics; sodium

### Citation Formats

```
Schile, Addison J., and Thompson, Ward H.
```*Tests for, origins of, and corrections to non-Gaussian statistics. The dipole-flip model*. United States: N. p., 2017.
Web. doi:10.1063/1.4981009.

```
Schile, Addison J., & Thompson, Ward H.
```*Tests for, origins of, and corrections to non-Gaussian statistics. The dipole-flip model*. United States. doi:10.1063/1.4981009.

```
Schile, Addison J., and Thompson, Ward H. Fri .
"Tests for, origins of, and corrections to non-Gaussian statistics. The dipole-flip model". United States.
doi:10.1063/1.4981009. https://www.osti.gov/servlets/purl/1465977.
```

```
@article{osti_1465977,
```

title = {Tests for, origins of, and corrections to non-Gaussian statistics. The dipole-flip model},

author = {Schile, Addison J. and Thompson, Ward H.},

abstractNote = {Linear response approximations are central to our understanding and simulations of nonequilibrium statistical mechanics. Despite the success of these approaches in predicting nonequilibrium dynamics, open questions remain. Laird and Thompson [J. Chem. Phys. 126, 211104 (2007)] previously formalized, in the context of solvation dynamics, the connection between the static linear-response approximation and the assumption of Gaussian statistics. The Gaussian statistics perspective is useful in understanding why linear response approximations are still accurate for perturbations much larger than thermal energies. In this study, we use this approach to address three outstanding issues in the context of the “dipole-flip” model, which is known to exhibit nonlinear response. First, we demonstrate how non-Gaussian statistics can be predicted from purely equilibrium molecular dynamics (MD) simulations (i.e., without resort to a full nonequilibrium MD as is the current practice). Second, we show that the Gaussian statistics approximation may also be used to identify the physical origins of nonlinear response residing in a small number of coordinates. Third, we explore an approach for correcting the Gaussian statistics approximation for nonlinear response effects using the same equilibrium simulation. Finally, the results are discussed in the context of several other examples of nonlinear responses throughout the literature.},

doi = {10.1063/1.4981009},

journal = {Journal of Chemical Physics},

number = 15,

volume = 146,

place = {United States},

year = {Fri Apr 21 00:00:00 EDT 2017},

month = {Fri Apr 21 00:00:00 EDT 2017}

}

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