On maximum entropy principle, superstatistics, power-law distribution and Renyi parameter

A.g Bashkirov

Physica A: Statistical Mechanics and its Applications, 2004, vol. 340, issue 1, 153-162

Abstract: The equilibrium distributions of probabilities are derived on the basis of the maximum entropy principle (MEP) for the Renyi and Tsallis entropies. New S-forms for the Renyi and Tsallis distribution functions are found which are normalised with corresponding entropies in contrast to the usual Z-forms normalised with partition functions Z. The superstatistics based on the Gibbs distribution of energy fluctuations gives rise to a distribution function of the same structure that the Renyi and Tsallis distributions have. The long-range “tail” of the Renyi distribution is the power-law distribution with the exponent −s expressed in terms of the free Renyi parameter q as s=1/(1−q). The condition s>0 gives rise to the requirement q<1. The parameter q can be uniquely determined with the use of a further extension of MEP as the condition for maximum of the difference between the Renyi and Boltzmann entropies for the same power-law distribution dependent on q. It is found that the maximum is realized for q within the range from 0.25 to 0.5 and the exponent s varies from 1.3 to 2 in dependence on parameters of stochastic systems.

Keywords: Renyi entropy; Zipf distribution; Temperature fluctuations (search for similar items in EconPapers)
Date: 2004
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437104004108
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:340:y:2004:i:1:p:153-162

DOI: 10.1016/j.physa.2004.04.002

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().