Physics Letters A 345 (2005) 231–236 www.elsevier.com/locate/pla Some remarks on non-extensive specific heat properties José Álvarez-Ramírez, Fracisco J. Valdés-Parada ∗ , J. Alberto Ochoa-Tapia Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico DF 09340, Mexico Received 23 May 2005; accepted 27 June 2005 Available online 11 July 2005 Communicated by J. Flouquet Abstract The aim of this Letter is to describe some relevant properties of specific heat derived from non-extensive statistics approach. It is shown that in the high- and low-temperature limits, the non-extensive specific heat displays the Dulong–Petit classical value 3R and a T 3 -dependence, respectively. The latter property implies, that in a strict sense, the non-extensive statistics approach can be unable to explain anomalous low-temperature behavior.  2005 Elsevier B.V. All rights reserved. Keywords: Specific heat; Debye theory; Non-extensive (Tsallis) statistics 1. Introduction For many materials, Debye theory [1] provides a good description of the specific heat (SH) C v behavior in a wide range of temperatures. Debye theory is able to describe two important asymptotic limits: (a) the high-temperature limit where the SH achieves the con- stant Dulong–Petit value 3R, where R is the universal gas constant, and (b) the low-temperature limit where the SH shows a T 3 -dependence. Besides, Debye the- ory predicts a monotonous increasing behavior of the SH with temperature. * Corresponding author. E-mail address: iqfv@xanum.uam.mx (F.J. Valdés-Parada). Deviations from the behavior predicted by the De- bye theory have been observed in the low-temperature region. Glasses at low temperature (below 2 K) show quasi-linear behavior (i.e., approximate linear depen- dence on temperature) [2]. In some compounds, the SH does not follow the Debye T 3 -dependence even above 2 K as in some cases maximum in C v /T 3 is observed around 10 K [3,4]. Some of the anom- alous properties have been explained by using soft potential model referring to an extension of tunneling model in which group of atoms can tunnel between same energy configurations [5]. It has been reported that the quasi-linear behavior or the maximum in SH can be explained by considering phason damping ef- fects [6]. Recently, it has been argued that it is possi- ble to explain some low-temperature SH anomalous 0375-9601/$ – see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2005.06.112