# Discrete Thermodynamics

## Abstract

Here, we consider the dependence of velocity probability distribution functions on the finite size of a thermodynamic system. We are motivated by applications to computational fluid dynamics, hence discrete thermodynamics. We then begin by describing a coarsening process that represents geometric renormalization. Then, based only on the requirements of conservation, we demonstrate that the pervasive assumption of local thermodynamic equilibrium is not form invariant. We develop a perturbative correction that restores form invariance to second-order in a small parameter associated with macroscopic gradients. Finally, we interpret the corrections in terms of unresolved kinetic energy and discuss the implications of our results both in theory and as applied to numerical simulation.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1406221

- Report Number(s):
- [LA-UR-17-23929]

[Journal ID: ISSN 0093-6413; TRN: US1703128]

- Grant/Contract Number:
- [AC52-06NA25396]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Mechanics Research Communications

- Additional Journal Information:
- [ Journal Volume: 93]; Journal ID: ISSN 0093-6413

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; nonequilibrium thermodynamics; computational fluid dynamics

### Citation Formats

```
Margolin, L. G., and Hunter, A. Discrete Thermodynamics. United States: N. p., 2017.
Web. doi:10.1016/j.mechrescom.2017.10.006.
```

```
Margolin, L. G., & Hunter, A. Discrete Thermodynamics. United States. doi:10.1016/j.mechrescom.2017.10.006.
```

```
Margolin, L. G., and Hunter, A. Wed .
"Discrete Thermodynamics". United States. doi:10.1016/j.mechrescom.2017.10.006. https://www.osti.gov/servlets/purl/1406221.
```

```
@article{osti_1406221,
```

title = {Discrete Thermodynamics},

author = {Margolin, L. G. and Hunter, A.},

abstractNote = {Here, we consider the dependence of velocity probability distribution functions on the finite size of a thermodynamic system. We are motivated by applications to computational fluid dynamics, hence discrete thermodynamics. We then begin by describing a coarsening process that represents geometric renormalization. Then, based only on the requirements of conservation, we demonstrate that the pervasive assumption of local thermodynamic equilibrium is not form invariant. We develop a perturbative correction that restores form invariance to second-order in a small parameter associated with macroscopic gradients. Finally, we interpret the corrections in terms of unresolved kinetic energy and discuss the implications of our results both in theory and as applied to numerical simulation.},

doi = {10.1016/j.mechrescom.2017.10.006},

journal = {Mechanics Research Communications},

number = ,

volume = [93],

place = {United States},

year = {2017},

month = {10}

}

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Web of Science

#### Figures / Tables:

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