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Erschienen in:
2015 | OriginalPaper | Buchkapitel
4. Various Statistical Ensembles
verfasst von : Isamu Kusaka
Erschienen in: Statistical Mechanics for Engineers
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Abstract
A canonical ensemble describes a system held at a constant temperature. From the canonical partition function follows the Helmholtz free energy. As we saw in thermodynamics, however, it is highly desirable to be able to describe a system held under a different set of constraints, such as constant temperature and pressure or constant temperature and chemical potentials of some species. These situations call for different free energies in thermodynamics, to which correspond different statistical ensembles in statistical mechanics. In this chapter, we construct such ensembles and illustrate their applications with several simple examples. Our first task is to establish the notion of microcanonical ensemble, which is suitable for describing an isolated system. The other ensembles of more practical importance, including the canonical ensemble, can be derived straightforwardly from the microcanonical ensemble.