Maximum entropy in a nonlinear system with a 1/f power spectrum

V.P. Koverda and V.N. Skokov

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 1, 21-28

Abstract: An analysis of master–slave hierarchy has been made in a system of nonlinear stochastic equations describing fluctuations with a 1/f spectrum at coupled nonequilibrium phase transitions. It is shown that for a system of stochastic equations there exist different probability distribution functions with power-law (non-Gaussian) and Gaussian tails. The governing equation of a system has a probability distribution function with Gaussian tails. Therefore, distribution functions for governing equations may be used for finding the Gibbs–Shannon entropy. The local maximum of this entropy has been found. It corresponds to the tuning of the parameters of the equations to criticality and points to the stability of fluctuations with a 1/f spectrum. The Tsallis entropy and the Renyi entropy for the probability distribution functions with power-law tails have been calculated. The parameter q, which is included in the determination of these entropies has been found from the condition that the coordinates of the maximum Gibbs–Shannon entropy coincide with the maxima of the Tsallis and Renyi entropies.

Keywords: 1/f noise; Stochastic equations; Maximum entropy principle; Self-organized criticality; Nonequilibrium phase transitions (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437111005620
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:391:y:2012:i:1:p:21-28

DOI: 10.1016/j.physa.2011.07.015

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 ().