# Deforming Gibbs Factor Using Tsallis q-Exponential with a Complex Parameter: An Ideal Bose Gas Case

## Abstract

**:**

## 1. Introduction

## 2. Starting Points

## 3. Calculations of Fugacity and Energy

## 4. Numerical Results and High-Temperature Behavior

## 5. Towards the Critical Point

## 6. The Limit of $\alpha \to 0$

## 7. Discussion

## 8. Materials and Methods

`wxMaxima 13.04.2`, a graphical interface for the computer algebra system MAXIMA (http://maxima.sourceforge.net). In particular, integrations are carried out by the Quadpack function

`quad_qagi`, see https://web.csulb.edu/~woollett/mbe8nint.pdf. Numerical equation solutions are obtained by the

`mnewton`procedure from the

`mnewton`package (https://web.csulb.edu/~woollett/mbe4solve.pdf).

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Fugacity for different values of s and $\alpha $ (with the real part fixed as ${\alpha}^{\prime}=0.1$). (

**left**) Real part ${z}^{\prime}=\mathrm{Re}z$. (

**right**) Imaginary part ${z}^{\u2033}=\mathrm{Im}z$.

**Figure 2.**Specific heat for different values of s and $\alpha $ (with the real part fixed as ${\alpha}^{\prime}=0.1$). (

**left**) Real part ${C}^{\prime}=\mathrm{Re}C$. (

**right**) Imaginary part ${C}^{\u2033}=\mathrm{Im}C$.

s, $\mathit{\alpha}=0.1+\mathit{i}{\mathit{\alpha}}^{\u2033}$ | ${\mathit{T}}_{\mathit{c}}$ | ${\mathit{z}}_{\mathit{c}}={\mathit{z}}_{\mathit{c}}^{\prime}+{\mathbf{iz}}_{\mathit{c}}^{\u2033}$ | $\mathit{C}/\mathit{N}$ at $\mathit{T}=\mathit{\infty}$ |
---|---|---|---|

$s=1$, ${\alpha}^{\u2033}=0.10$ | 0 | 1 | $1.176+0.294i$ |

$s=2$, ${\alpha}^{\u2033}=0$ | 0.690 | 1 | 2.857 |

$s=2$, ${\alpha}^{\u2033}=0.10$ | 0.616 | $1.246-0.0041i$ | $2.414+1.034i$ |

$s=2$, ${\alpha}^{\u2033}=0.12$ | 0.612 | $1.313-0.0061i$ | $2.260+1.162i$ |

$s=2$, ${\alpha}^{\u2033}=0.15$ | 0.609 | $1.427-0.0138i$ | $2.022+1.300i$ |

$s=3$, ${\alpha}^{\u2033}=0.10$ | 0.359 | $7.222-1.371i\phantom{0}$ | $3.462+2.308i$ |

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Rovenchak, A.
Deforming Gibbs Factor Using Tsallis *q*-Exponential with a Complex Parameter: An Ideal Bose Gas Case. *Symmetry* **2020**, *12*, 732.
https://doi.org/10.3390/sym12050732

**AMA Style**

Rovenchak A.
Deforming Gibbs Factor Using Tsallis *q*-Exponential with a Complex Parameter: An Ideal Bose Gas Case. *Symmetry*. 2020; 12(5):732.
https://doi.org/10.3390/sym12050732

**Chicago/Turabian Style**

Rovenchak, Andrij.
2020. "Deforming Gibbs Factor Using Tsallis *q*-Exponential with a Complex Parameter: An Ideal Bose Gas Case" *Symmetry* 12, no. 5: 732.
https://doi.org/10.3390/sym12050732