Ensemble equivalence for general many-body systems

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.

v1: 5 pages, 1 figure; v2: minor corrections, references updated; v3: minor corrections, close to version published in EPL

References in corpus (6)

• The large deviation approach to statistical mechanics
• Statistical mechanics and dynamics of solvable models with long-range interactions
• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
• Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
• Nonequivalence of ensembles for long-range quantum spin systems in optical lattices

Cited by in corpus (20)

• Nonequilibrium Markov processes conditioned on large deviations
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Liquid-Gas phase transition in nuclei
• Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges
• Eigenstate thermalization from the clustering property of correlation
• The grand canonical catastrophe as an instance of condensation of fluctuations
• Equivalence of nonequilibrium ensembles in turbulence models
• Tsallis entropy induced metrics and CAT(k) spaces
• Continuum of classical-field ensembles from canonical to grand canonical and the onset of their equivalence
• Ensemble inequivalence : Landau theory and the ABC model
• Conditional reversibility in nonequilibrium stochastic systems
• Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian
• Microcanonical analysis of the Curie-Weiss anisotropic quantum Heisenberg model in a magnetic field
• Tsallis entropy composition and the Heisenberg group
• On the fluctuations of the number of atoms in the condensate
• Poles, Shocks and Tygers: The Time-reversible Burgers equation
• Effective dynamics of a conditioned generalized linear Glauber model
• Thermodynamics and phase transitions of black holes in contact with a gravitating heat bath