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Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches

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  • Ervin Kaminski Lenzi

    (Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Gen. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, Brazil
    National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro 22290-180, RJ, Brazil)

  • Luiz Roberto Evangelista

    (Departmento de Física, Universidade Estadual de Maringá, Av. Colombo 5790, Maringá 87020-900, PR, Brazil)

  • Luciano Rodrigues da Silva

    (National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro 22290-180, RJ, Brazil
    Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil)

Abstract

We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and the other considers the extension of the concept of entropy, i.e., the Tsallis statistics. We reviewed and discussed some of the main properties of these approaches and used the thermal Green function formalism to perform the developments, simultaneously allowing us to analyze each case’s dynamics and thermodynamics aspects. In particular, the results allow us to understand how the extensions change the behavior of some quantities, particularly fluctuations related to the system.

Suggested Citation

  • Ervin Kaminski Lenzi & Luiz Roberto Evangelista & Luciano Rodrigues da Silva, 2023. "Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2777-:d:1174965
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    References listed on IDEAS

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    1. E. K. Lenzi & B. F. de Oliveira & N. G.C. Astrath & L. C. Malacarne & R. S. Mendes & M. L. Baesso & L. R. Evangelista, 2008. "Fractional approach, quantum statistics, and non-crystalline solids at very low temperatures," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(2), pages 155-158, March.
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