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Nonlocal statistical mechanics: General fractional Liouville equations and their solutions

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  • Tarasov, Vasily E.

Abstract

Nonlocal generalization of classical statistical mechanics is proposed by using the general fractional calculus in the Luchko form. Some basic concepts of nonlocal statistical mechanics in Liouville picture are suggested. Nonlocal analogs of the standard law of probability conservation are suggested in integral and differential forms. Nonlocality is described by the pairs of Sonin kernels that belong to the Luchko set. Examples of solutions of general fractional Liouville equations are proposed for power-law nonlocality in phase space. The introduction gives a brief overview of some approaches to the description of nonlocal statistical mechanics.

Suggested Citation

  • Tarasov, Vasily E., 2023. "Nonlocal statistical mechanics: General fractional Liouville equations and their solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    • Handle: RePEc:eee:phsmap:v:609:y:2023:i:c:s0378437122009244
    DOI: 10.1016/j.physa.2022.128366
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    References listed on IDEAS

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    1. Yuri Luchko, 2022. "Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense," Mathematics, MDPI, vol. 10(6), pages 1-24, March.
    2. Tarasov, Vasily E., 2021. "Nonlocal quantum system with fractal distribution of states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
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    15. Tarasov, Vasily E., 2015. "Fractional Liouville equation on lattice phase-space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 330-342.
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    1. Vasily E. Tarasov, 2023. "General Fractional Calculus in Multi-Dimensional Space: Riesz Form," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    2. Vasily E. Tarasov, 2023. "Multi-Kernel General Fractional Calculus of Arbitrary Order," Mathematics, MDPI, vol. 11(7), pages 1-32, April.
    3. Vasily E. Tarasov, 2023. "General Fractional Noether Theorem and Non-Holonomic Action Principle," Mathematics, MDPI, vol. 11(20), pages 1-35, October.
    4. 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.
    5. Mohammed Al-Refai & Yuri Luchko, 2023. "The General Fractional Integrals and Derivatives on a Finite Interval," Mathematics, MDPI, vol. 11(4), pages 1-13, February.

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