Ensemble equivalence for general many-body systems

2011/06/30 by Hugo Touchette · 1 voice · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1209/0295-5075/96/50010

published as Europhys. Lett. 96, 50010, 2011 · v1: 5 pages, 1 figure; v2: minor corrections, references updated; v3: minor corrections, close to version published in EPL

arxiv created 2011/11/15 · openalex publication_date 2011/11/25 · arxiv updated 2011/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

It has been proved for a class of mean-field and long-range systems that the concavity of the thermodynamic entropy determines whether the microcanonical and canonical ensembles are equivalent at the level of their equilibrium states, i.e., whether they give rise to the same equilibrium states. Here we show that this correspondence is actually a general result of statistical mechanics: it holds for any many-body system for which equilibrium states can be defined and in principle calculated. The same correspondence applies for other dual statistical ensembles, such as the canonical and grand-canonical ensembles.

Citations

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Complete analysis of phase transitions and ensemble equivalence for the Curie–Weiss–Potts model
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume–Emery–Griffiths model
• An introduction to the thermodynamic and macrostate levels of nonequivalent ensembles

Cited by

• Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges

Discussions

• I am puzzled about the equivalence between different ensembles in statistical mechanics (microcanonical, canonical, grand canonical). In microcanonical ensemble(ME), the system is isolated, so the $(E [stackexchange, 1 points]

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• Reconnecting statistical physics and combinatorics beyond ensemble equivalence