Physica A 317 (2003) 199–208 www.elsevier.com/locate/physa Bose–Einstein and Fermi–Dirac distributions in nonextensive Tsallis statistics: an exact study H.H. Arag˜ ao-Rˆ ego a , D.J. Soares a , L.S. Lucena a , L.R. da Silva a; b , E.K. Lenzi c ; ∗ , Kwok Sau Fa d a International Center for Complex Systems and Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN, Brazil b Center for Polymer Studies, Boston University, Boston, MA 02215, USA c Centro Brasileiro de Pesquisas F sicas, R. Xavier Sigaud, 150, 22290-180 Rio de Janeiro, Brazil d Departamento de F sica, Universidade Estadual de Maring a Av. Colombo 5790, 87020-900 Maring a-PR, Brazil Received 2 May 2002 Abstract Generalized Bose–Einstein and Fermi–Dirac distributions are analyzed in nonextensive Tsallis statistics by considering the normalized constraints in the eective temperature approach. These distributions are worked in D-dimension by employing a general density of states g() ˙   D-1 (  D = D= 2+ D=n and  D¿ 0). Thermodynamic functions such as internal energy and average number of particles are also obtained in this context. c  2002 Elsevier Science B.V. All rights reserved. PACS: 05.30.-d; 03.75.Fi Keywords: Bose–Einstein; Fermi–Dirac; Nonextensive; Tsallis statistics 1. Introduction The recent proposal to generalize the usual Boltzmann-Gibbs statistical mechanics, based on the following nonextensive entropy [1–3] 1 S q = 1 - Tr  q q q - 1 ; (1) ∗ Corresponding author. Fax: +55-21-586-7400. E-mail address: eklenzi@cbpf.br (E.K. Lenzi). 1 See http://tsallis.cat.cbpf.br/biblio.htm for a periodically updated bibliography on the subject; a set of minireviews appeared in Ref. [2]. 0378-4371/03/$-see front matter c  2002 Elsevier Science B.V. All rights reserved. PII:S0378-4371(02)01330-4