Intensive variables and fluctuations in non-extensive thermodynamics: the generalized Gibbs-Duhem equation and Einstein's formula

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  • 21 June 2001
Abstract
Two questions which are still under discussion in the framework of Tsallis statistics are considered: the definition of intensive variables and the calculation of fluctuations. We first present a generalization of the Gibbs-Duhem equation, which suggests a transformation of variables that allows standard thermodynamics to be recovered. Secondly, we derive a generalization of Einstein's formula for the probability of a fluctuation to occur. The use of the proposed transformation of variables suggests that fluctuations within Tsallis statistics can be mapped to those of standard statistical mechanics.

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