Eur. Phys. J. B 47, 557-561 (2005)
https://doi.org/10.1140/epjb/e2005-00356-3

A non self-referential expression of Tsallis' probability distribution function

¹ Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan
² Istituto Nazionale di Fisica della Materia (INFM) and Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Corresponding authors: ^a wada@ee.ibaraki.ac.jp - ^b antonio.scarfone@polito.it

Received: 17 February 2005
Revised: 22 July 2005
Published online: 17 November 2005

Abstract

The canonical probability distribution function (pdf) obtained by optimizing the Tsallis entropy under either the linear mean energy constraint U or the escort mean energy constraint U_q suffer self-referentiality. In a recent paper [Phys. Lett. A 335, 351 (2005)] the authors have shown that the pdfs obtained with either U or U_q are equivalent to the pdf in a non self-referential form. Based on this result we derive an alternative expression for the Tsallis distributions, employing either U or U_q, which is non self-referential.