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Title
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The q-exponential family in statistical physics
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Author
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Abstract
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| The Boltzmann-Gibbs probability distribution, seen as a statistical model, belongs to the exponential family. Recently, the latter concept has been generalized. The q-exponential family has been shown to be relevant for the statistical description of small isolated systems. Two main applications are reviewed: 1. The distribution of the momentum of a single particle is a q-Gaussian, the distribution of its velocity is a deformed Maxwellian; 2. The configurational density distribution belongs to the q-exponential family. The definition of the temperature of small isolated systems is discussed. It depends on defining the thermodynamic entropy of a microcanonical ensemble in a suitable manner. The simple example of non-interacting harmonic oscillators shows that Rényi's entropy functional leads to acceptable results. |
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Language
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English
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Source (journal)
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Journal of physics : conference series. - Bristol, 2004, currens
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Source (book)
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Proceedings of Kyoto RIMS Workshop Mathematical Aspects of Generalized Entropies and their Applications / Suyari, H. [edit.]; et al. [edit.]
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Publication
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Bristol
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Institute of Physics Publishing
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2010
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ISSN
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1742-6588
[print]
1742-6596
[online]
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Volume/pages
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201
:1
(2010)
, p. 012003,1-012003,11
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Full text (Publisher's DOI)
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Full text (open access)
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