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A classification of nonequilibrium steady states based on temperature correlations

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  • Davis, Sergio

Abstract

Although generalized ensembles have now been in use in statistical mechanics for decades, including frameworks such as Tsallis’ nonextensive statistics and superstatistics, a classification of these generalized ensembles outlining the boundaries of validity of different families of models, is still lacking. In this work, such a classification is proposed in terms of supercanonical and subcanonical ensembles, according to a newly defined parameter, the inverse temperature covariance parameter U. This parameter is non-negative in superstatistics (and is equal to the variance of the inverse temperature) but can be negative for other families of statistical ensembles, acquiring then a broader meaning. It is shown that U is equal for every region of a composite system in a steady state, and examples are given of supercanonical and subcanonical states.

Suggested Citation

  • Davis, Sergio, 2022. "A classification of nonequilibrium steady states based on temperature correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    • Handle: RePEc:eee:phsmap:v:608:y:2022:i:p1:s037843712200807x
    DOI: 10.1016/j.physa.2022.128249
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    References listed on IDEAS

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    1. Umpierrez, Haridas & Davis, Sergio, 2021. "Fluctuation theorems in q-canonical ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    2. Atenas, Boris & Curilef, Sergio, 2021. "A statistical description for the Quasi-Stationary-States of the dipole-type Hamiltonian Mean Field Model based on a family of Vlasov solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    3. Davis, Sergio & Gutiérrez, Gonzalo, 2019. "Emergence of Tsallis statistics as a consequence of invariance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    4. Plastino, A. & Monteoliva, D. & Rocca, M.C., 2022. "Tsallis’ statistics for long range interactions: Gravity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    5. Davis, Sergio, 2022. "Fluctuating temperature outside superstatistics: Thermodynamics of small systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    6. Benjamin Schäfer & Christian Beck & Kazuyuki Aihara & Dirk Witthaut & Marc Timme, 2018. "Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics," Nature Energy, Nature, vol. 3(2), pages 119-126, February.
    7. Ispolatov, I & Cohen, E.G.D, 2001. "On first-order phase transitions in microcanonical and canonical non-extensive systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 475-487.
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    Cited by:

    1. Constanza Farías & Sergio Davis, 2023. "Temperature distribution in finite systems: application to the one-dimensional Ising chain," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(3), pages 1-10, March.

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