The equivalence of ensembles and the Gibbs phase rule for classical lattice systems |
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Authors: | Anders Martin-Löf |
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Affiliation: | (1) Department of Mathematics, University of Stockholm, Stockholm, Sweden |
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Abstract: | We study the relation between the microcanonical, canonical, and grand canonical ensembles in the thermodynamic limit when the system becomes infinite. They are equivalent if there is only one phase in the system. In general it is shown that there is a unique limit of the microcanonical state being a mixture of pure phases if the microcanonical restrictions determine the volume fractions of the phases uniquely, and then the Gibbs phase rule is valid. In this context we show how to define the set of order parameters associated with the state of the system in a natural way. |
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Keywords: | Equivalence of different ensembles order parameters equilibrium states pure phases variational principles convexity |
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