Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-06-06
Physics
Condensed Matter
Statistical Mechanics
20 pages, no figures, the disappeared "primes" on the distributions are added. Also, Eq. (65) is corrected
Scientific paper
10.1103/PhysRevE.66.046134
The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Renyi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.
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