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Temperature distribution in finite systems: application to the one-dimensional Ising chain

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  • Constanza Farías

    (Universidad Andres Bello)

  • Sergio Davis

    (Universidad Andres Bello
    Matter and Complexity (P2mc), Comisión Chilena de Energía Nuclear)

Abstract

Thermodynamic studies of small systems interacting with a finite environment display an interesting statistical behavior, similar to complex non-equilibrium systems. In both situations there are several applicable definitions of inverse temperature, either intrinsic or dependent of the statistical ensemble, and uncertainty in these quantities has to be taken into account. In this work we develop these concepts using as an example an isolated one-dimensional Ising chain subsystem that does not follow the canonical distribution. In the context of this example, we explicitly show that the theory of superstatistics cannot describe the behavior of the subsystem, and verify a recently reported relation between the ensemble and microcanonical inverse temperatures. Our results hint at a new framework for dealing with regions of microcanonical systems with positive heat capacity, which should be described by some new class of statistical ensembles outside superstatistics but still preserving the notion of temperature uncertainty.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:eurphb:v:96:y:2023:i:3:d:10.1140_epjb_s10051-023-00509-y
    DOI: 10.1140/epjb/s10051-023-00509-y
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    References listed on IDEAS

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    1. Chung, Won Sang & Hassanabadi, Hassan, 2019. "Statistical physics when the heat bath is large but finite," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    2. Moreno, Felipe & Davis, Sergio & Loyola, Claudia & Peralta, Joaquín, 2018. "Ordered metastable states in the Potts model and their connection with the superheated solid state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 361-368.
    3. Davis, Sergio, 2022. "Fluctuating temperature outside superstatistics: Thermodynamics of small systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    4. Farías, Constanza & Davis, Sergio, 2021. "Multiple metastable states in an off-lattice Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    5. Davis, Sergio, 2022. "A classification of nonequilibrium steady states based on temperature correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    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.
    Full references (including those not matched with items on IDEAS)

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