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An introduction to the thermodynamic and macrostate levels of nonequivalent ensembles

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  • Touchette, Hugo
  • Ellis, Richard S.
  • Turkington, Bruce

Abstract

This short paper presents a nontechnical introduction to the problem of nonequivalent microcanonical and canonical ensembles. Both the thermodynamic and the macrostate levels of definition of nonequivalent ensembles are introduced. The many relationships that exist between these two levels are also explained in simple physical terms.

Suggested Citation

  • Touchette, Hugo & Ellis, Richard S. & Turkington, Bruce, 2004. "An introduction to the thermodynamic and macrostate levels of nonequivalent ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 138-146.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:138-146
    DOI: 10.1016/j.physa.2004.03.088
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    References listed on IDEAS

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    1. Lynden-Bell, D., 1999. "Negative specific heat in astronomy, physics and chemistry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 293-304.
    2. Borges, Ernesto P & Tsallis, Constantino, 2002. "Negative specific heat in a Lennard-Jones-like gas with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 148-151.
    3. Ellis, Richard S. & Touchette, Hugo & Turkington, Bruce, 2004. "Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume–Emery–Griffiths model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 518-538.
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    Citations

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    Cited by:

    1. Gorban, Alexander, 2007. "Order–disorder separation: Geometric revision," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 85-102.
    2. Matty, Michael & Lancaster, Lachlan & Griffin, William & Swendsen, Robert H., 2017. "Comparison of canonical and microcanonical definitions of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 474-489.
    3. Touchette, H. & Costeniuc, M. & Ellis, R.S. & Turkington, B., 2006. "Metastability within the generalized canonical ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 132-137.
    4. Casetti, Lapo & Kastner, Michael, 2007. "Partial equivalence of statistical ensembles and kinetic energy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 318-334.
    5. Großkinsky, Stefan, 2008. "Equivalence of ensembles for two-species zero-range invariant measures," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1322-1350, August.

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