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 ${\beta }^{BG}$ replaced by its value $\frac{1}{k_{B}T}$. They are obtained within the finite heat bath canonical ensemble approach. Furthermore, we discuss the meaning of the Lagrange multiplier of the generalized framework, ${\beta }^T$, and show that the entropy found here is just the Rènyi entropy plus a definite constant.

17 pages, results improved, dicussion on Lagrange multipliers added, references added

References in corpus (11)

• Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and Lévy distributions
• Generalized entropies from first principles
• Ideal gas in nonextensive optimal Lagrange multipliers formalism
• Thermodynamics' 0-th-Law in a nonextensive scenario
• An extended-phase-space dynamics for the generalized nonextensive thermostatistics
• Tsallis Statistics: Averages and a Physical Interpretation of the Lagrange Multiplier $\beta$
• Nonextensive methods in turbulence and particle physics
• Equipartition and Virial theorems in a nonextensive optimal Lagrange multipliers scenario
• Self-organized criticality in atmospheric cascades
• Quasicanonical Gibbs distribution and Tsallis nonextensive statistics
• Microscopic analog of temperature within nonextensive thermostatistics

Cited by in corpus (3)

• An additive variant of Tsallis generalized entropy
• Numerical calculation of the energy relative fluctuation for a system in contact with a finite heat bath
• A generalized thermodynamics for power-law statistics