# Phase transition and entropy inequality of noncommutative black holes in a new extended phase space

## Abstract

We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as the noncommutative pressure . In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. the former dominates the UV regime while the latter does the IR regime, respectively. In addition, by means of the reverse isoperimetric inequality, we indicate that only the black hole with the Gaussian smeared matter distribution holds the maximum entropy for a given thermodynamic volume among the noncommutative black holes with various matter distributions.

- Authors:

- School of Physics, Nankai University, Tianjin 300071 (China)

- Publication Date:

- OSTI Identifier:
- 22679956

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 03; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANTI DE SITTER SPACE; BLACK HOLES; COSMOLOGICAL CONSTANT; DISTRIBUTION; ENTROPY; PHASE SPACE; PHASE TRANSFORMATIONS; SCHWARZSCHILD METRIC; THERMODYNAMICS

### Citation Formats

```
Miao, Yan-Gang, and Xu, Zhen-Ming, E-mail: miaoyg@nankai.edu.cn, E-mail: xuzhenm@mail.nankai.edu.cn.
```*Phase transition and entropy inequality of noncommutative black holes in a new extended phase space*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/03/046.

```
Miao, Yan-Gang, & Xu, Zhen-Ming, E-mail: miaoyg@nankai.edu.cn, E-mail: xuzhenm@mail.nankai.edu.cn.
```*Phase transition and entropy inequality of noncommutative black holes in a new extended phase space*. United States. doi:10.1088/1475-7516/2017/03/046.

```
Miao, Yan-Gang, and Xu, Zhen-Ming, E-mail: miaoyg@nankai.edu.cn, E-mail: xuzhenm@mail.nankai.edu.cn. Wed .
"Phase transition and entropy inequality of noncommutative black holes in a new extended phase space". United States.
doi:10.1088/1475-7516/2017/03/046.
```

```
@article{osti_22679956,
```

title = {Phase transition and entropy inequality of noncommutative black holes in a new extended phase space},

author = {Miao, Yan-Gang and Xu, Zhen-Ming, E-mail: miaoyg@nankai.edu.cn, E-mail: xuzhenm@mail.nankai.edu.cn},

abstractNote = {We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as the noncommutative pressure . In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. the former dominates the UV regime while the latter does the IR regime, respectively. In addition, by means of the reverse isoperimetric inequality, we indicate that only the black hole with the Gaussian smeared matter distribution holds the maximum entropy for a given thermodynamic volume among the noncommutative black holes with various matter distributions.},

doi = {10.1088/1475-7516/2017/03/046},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2017,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2017},

month = {Wed Mar 01 00:00:00 EST 2017}

}