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Heat and entropy in nonextensive thermodynamics: transmutation from Tsallis theory to Rényi-entropy-based theory

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  • Abe, Sumiyoshi

Abstract

Macroscopic nonextensive thermodynamics is studied without recourse to microscopic statistical mechanics. Taking the Tsallis entropy as an example, it is shown that the concept of the physical temperature introduced through the generalized zeroth law of thermodynamics necessarily leads to modification of Clausius’ definition of the thermodynamic entropy. It is also shown, by applying this generalized Clausius entropy to a composite nonextensive system, how the entropy and the quantity of heat behave in an arbitrary thermodynamic process. The results presented here indicate that, even starting with a nonextensive entropy, the thermodynamic entropy appearing at the macroscopic level has to be extensive, in accordance with Carathéodory's theorem. This fact can be observed as transmutation from nonextensive Tsallis theory to extensive Rényi-entropy-based theory.

Suggested Citation

  • Abe, Sumiyoshi, 2001. "Heat and entropy in nonextensive thermodynamics: transmutation from Tsallis theory to Rényi-entropy-based theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 417-423.
    • Handle: RePEc:eee:phsmap:v:300:y:2001:i:3:p:417-423
    DOI: 10.1016/S0378-4371(01)00348-X
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    Cited by:

    1. Masamichi Ishihara, 2023. "Thermodynamic quantities of independent harmonic oscillators in microcanonical and canonical ensembles in the Tsallis statistics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(1), pages 1-12, January.
    2. Evangelista, L.R. & Lenzi, E.K. & Barbero, G. & Scarfone, A.M., 2024. "On the Einstein–Smoluchowski relation in the framework of generalized statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 635(C).
    3. Masamichi Ishihara, 2022. "Thermodynamics of the independent harmonic oscillators with different frequencies in the Tsallis statistics in the high physical temperature approximation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(3), pages 1-10, March.
    4. Ishihara, Masamichi, 2021. "Derivation of the density operator with quantum analysis for the generalized Gibbs ensemble in quantum statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).

    More about this item

    Keywords

    Nonextensive thermodynamics;

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