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arXiv · 0911.5392

The q-exponential family in statistical physics

Jan Naudts
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Abstract

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 Renyi's entropy functional leads to acceptable results.

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Jan Naudts. 2009-11-28. The q-exponential family in statistical physics. https://doi.org/10.1088/1742-6596%2F201%2F1%2F012003

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