Thermodynamics arising from Tsallis' thermostatistics

Abstract

We show, in two different ways, that the Tsallis' partition function and its derivatives are related to thermodynamic quantities such as entropy, internal energy, etc., in the same way as in Boltzmann-Gibbs' formalism, with the Lagrange multiplier $β^{BG}$ replaced by its value $\frac{1}{k_BT}$. They are obtained within the finite heat bath canonical ensemble approach. Furthermore, we discuss the meaning of the Lagrange multiplier of the generalized framework, $β^T$, and show that the entropy found here is just the Rènyi entropy plus a definite constant.