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Non-Extensivity of the Configurational Density Distribution in the Classical Microcanonical Ensemble

Departement Natuurkunde, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen, Belgium
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Entropy 2009, 11(2), 285-294; https://doi.org/10.3390/e11020285
Received: 7 May 2009 / Accepted: 9 June 2009 / Published: 11 June 2009
We show that the configurational probability distribution of a classical gas always belongs to the q-exponential family. One of the consequences of this observation is that the thermodynamics of the configurational subsystem is uniquely determined up to a scaling function. As an example we consider a system of non-interacting harmonic oscillators. In this example, the scaling function can be determined from the requirement that in the limit of large systems the microcanonical temperature of the configurational subsystem should coincide with that of the canonical ensemble. The result suggests that R´enyi’s entropy function is the relevant one rather than that of Tsallis. View Full-Text
Keywords: microcanonical ensemble; Tsallis entropy; R´enyi entropy; q-exponential distribution microcanonical ensemble; Tsallis entropy; R´enyi entropy; q-exponential distribution
MDPI and ACS Style

Naudts, J.; Baeten, M. Non-Extensivity of the Configurational Density Distribution in the Classical Microcanonical Ensemble. Entropy 2009, 11, 285-294.

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