# The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics

## Abstract

We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible correlation in the area of quantum phase transitions is a major motivation for this research. We extend a representation of the irreducible correlation from finite temperatures to absolute zero.

- Authors:

- Max-Planck-Institute for Mathematics in the Sciences, Inselstraße 22, D-04103 Leipzig (Germany)

- Publication Date:

- OSTI Identifier:
- 22390861

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1641; Journal Issue: 1; Conference: MAXENT 2014: Conference on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Clos Luce, Amboise (France), 21-26 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; ENTROPY; GEODESICS; GEOMETRY; IRREDUCIBLE REPRESENTATIONS; PHASE TRANSFORMATIONS; QUANTUM MECHANICS

### Citation Formats

```
Weis, Stephan.
```*The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics*. United States: N. p., 2015.
Web. doi:10.1063/1.4905976.

```
Weis, Stephan.
```*The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics*. United States. doi:10.1063/1.4905976.

```
Weis, Stephan. Tue .
"The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics". United States.
doi:10.1063/1.4905976.
```

```
@article{osti_22390861,
```

title = {The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics},

author = {Weis, Stephan},

abstractNote = {We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible correlation in the area of quantum phase transitions is a major motivation for this research. We extend a representation of the irreducible correlation from finite temperatures to absolute zero.},

doi = {10.1063/1.4905976},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1641,

place = {United States},

year = {Tue Jan 13 00:00:00 EST 2015},

month = {Tue Jan 13 00:00:00 EST 2015}

}

DOI: 10.1063/1.4905976

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