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Fluctuating temperature outside superstatistics: Thermodynamics of small systems

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  • Davis, Sergio

Abstract

The existence of fluctuations of temperature has been a somewhat controversial topic in thermodynamics but nowadays it is recognized that they must be taken into account in small, finite systems. Although for nonequilibrium steady states superstatistics is becoming the de facto framework for expressing such temperature fluctuations, some recent results put into question the idea of temperature as a phase space observable. In this work we present and explore the statistics that describes a part of an isolated system, small enough to have well-defined uncertainties in energy and temperature, but lacking a superstatistical description. These results motivate the use of the so-called fundamental temperature as an observable and may be relevant for the statistical description of small systems in physical chemistry.

Suggested Citation

  • Davis, Sergio, 2022. "Fluctuating temperature outside superstatistics: Thermodynamics of small systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    • Handle: RePEc:eee:phsmap:v:589:y:2022:i:c:s0378437121009018
    DOI: 10.1016/j.physa.2021.126665
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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. Gravanis, E. & Akylas, E. & Michailides, C. & Livadiotis, G., 2021. "Superstatistics and isotropic turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(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. 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.
    5. Touchette, Hugo, 2002. "When is a quantity additive, and when is it extensive?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 84-88.
    6. Davis, Sergio & Gutiérrez, Gonzalo, 2018. "Temperature is not an observable in superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 864-870.
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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.
    2. Davis, Sergio, 2022. "A classification of nonequilibrium steady states based on temperature correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).

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