We discuss the Tsallis entropy in finite -unit nonextensive systems by using the multivariate -Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the -average (: the entropic index). The Tsallis entropy obtained by the -average has an exponential dependence: for large . In contrast, the Tsallis entropy obtained by the normal average is given by for large . dependences of the Tsallis entropy obtained by the - and normal averages are generally quite different, although both results are in fairly good agreement for . The validity of the factorization approximation (FA) to PDFs, which has been commonly adopted in the literature, has been examined. We have calculated correlations defined by for where , and the bracket stands for the normal and -averages. The first-order correlation expresses the intrinsic correlation and higher-order correlations with include nonextensivity-induced correlation, whose physical origin is elucidated in the superstatistics.
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September 2010
Research Article|
September 07 2010
The entropy in finite -unit nonextensive systems: The normal average and -average
Hideo Hasegawa
Hideo Hasegawa
a)
Department of Physics,
Tokyo Gakugei University
, Koganei, Tokyo 184-8501, Japan
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a)
Electronic addresses: [email protected] and [email protected].
J. Math. Phys. 51, 093301 (2010)
Article history
Received:
May 16 2010
Accepted:
July 23 2010
Citation
Hideo Hasegawa; The entropy in finite -unit nonextensive systems: The normal average and -average. J. Math. Phys. 1 September 2010; 51 (9): 093301. https://doi.org/10.1063/1.3479394
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