### Abstract

By only requiring the q deformed logarithms (q exponentials) to possess arguments chosen from the entire set of positive real numbers (all real numbers), we show that the q-logarithm (q exponential) can be written in such a way that its argument varies between 0 and 1 (among negative real numbers) for 1 ≤ q <2, while the interval 0 <q ≤ 1 corresponds to any real argument greater than 1 (positive real numbers). These two distinct intervals of the nonextensivity index q, also the expressions of the deformed functions associated with them, are related to one another through the relation (2 - q), which is so far used to obtain the ordinary stationary distributions from the corresponding escort distributions, and vice versa in an almost ad hoc manner. This shows that the escort distributions are only a means of extending the interval of validity of the deformed functions to the one of ordinary, undeformed ones. Moreover, we show that, since the Tsallis entropy is written in terms of the q-logarithm and its argument, being the inverse of microstate probabilities, takes values equal to or greater than 1, the resulting stationary solution is uniquely described by the one obtained from the ordinary constraint. Finally, we observe that even the escort stationary distributions can be obtained through the use of the ordinary averaging procedure if the argument of the q-exponential lies in (- ∞, 0]. However, this case corresponds to, although related, a different entropy expression than the Tsallis entropy.

Original language | English |
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Pages (from-to) | 2225-2229 |

Number of pages | 5 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 374 |

Issue number | 22 |

DOIs | |

Publication status | Published - May 3 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

- Escort average
- Ordinary average
- q-exponential
- q-logarithm
- Tsallis entropy

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**The maximization of Tsallis entropy with complete deformed functions and the problem of constraints.** / Oikonomou, Thomas; Bagci, G. Baris.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 374, no. 22, pp. 2225-2229. https://doi.org/10.1016/j.physleta.2010.03.038

}

TY - JOUR

T1 - The maximization of Tsallis entropy with complete deformed functions and the problem of constraints

AU - Oikonomou, Thomas

AU - Bagci, G. Baris

PY - 2010/5/3

Y1 - 2010/5/3

N2 - By only requiring the q deformed logarithms (q exponentials) to possess arguments chosen from the entire set of positive real numbers (all real numbers), we show that the q-logarithm (q exponential) can be written in such a way that its argument varies between 0 and 1 (among negative real numbers) for 1 ≤ q <2, while the interval 0

AB - By only requiring the q deformed logarithms (q exponentials) to possess arguments chosen from the entire set of positive real numbers (all real numbers), we show that the q-logarithm (q exponential) can be written in such a way that its argument varies between 0 and 1 (among negative real numbers) for 1 ≤ q <2, while the interval 0

KW - Escort average

KW - Ordinary average

KW - q-exponential

KW - q-logarithm

KW - Tsallis entropy

UR - http://www.scopus.com/inward/record.url?scp=77950595479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950595479&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2010.03.038

DO - 10.1016/j.physleta.2010.03.038

M3 - Article

VL - 374

SP - 2225

EP - 2229

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 22

ER -