Thermostatistical aspects of generalized entropies

✍ Scribed by K.S. Fa; E.K. Lenzi

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 274 KB
• Volume: 20
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(03)00369-2

✦ Synopsis

We investigate the properties concerning a class of generalized entropies given by S q;r ¼ kf1 À ½ P i p q i r g=½rðq À 1Þ which include TsallisÕ entropy (r ¼ 1), the usual Boltzmann-Gibbs entropy (q ¼ 1), R e enyiÕs entropy (r ¼ 0) and normalized TsallisÕ entropy (r ¼ À1). In order to obtain the generalized thermodynamic relations we use the laws of thermodynamics and considering the hypothesis that the joint probability of two independent systems is given by p

We show that the transmutation which occurs from TsallisÕ entropy to R e enyiÕs entropy also occur with S q;r . In this scenario, we also analyze the generalized variance, covariance and correlation coefficient of a non-interacting system by using extended optimal Lagrange multiplier approach. We show that the correlation coefficient tends to zero in the thermodynamic limit. However, R e enyiÕs entropy related to this non-interacting system presents a certain degree of non-extensivity.