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

Thomas Oikonomou, G. Baris Bagci

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

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 languageEnglish
Pages (from-to)2225-2229
Number of pages5
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume374
Issue number22
DOIs
Publication statusPublished - May 3 2010

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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