This article is cited in 5 papers

Theoretical and Mathematical Physics

Entropy maximum in a nonlinear system with the $1/f$ fluctuation spectrum

V. P. Koverda, V. N. Skokov

Institute of Thermal Physics, Ural Branch, Russian Academy of Sciences, Ekaterinburg

Abstract: Analysis of the control and subordination is carried out for the system of nonlinear stochastic equations describing fluctuations with the $1/f$ spectrum and with the interaction of nonequilibrium phase transitions. It is shown that the control equation of the system has a distribution function that decreases upon an increase in the argument in the same way as the Gaussian distribution function. Therefore, this function can be used for determining the Gibbs–Shannon informational entropy. The local maximum of this entropy is determined, which corresponds to tuning of the stochastic equations to criticality and indicates the stability of fluctuations with the $1/f$ spectrum. The values of parameter q appearing in the definition of these entropies are determined from the condition that the coordinates of the Gibbs–Shannon entropy maximum coincide with the coordinates of the Tsallis entropy maximum and the Renyi entropy maximum for distribution functions with a power dependence.

Received: 29.03.2011

 English version: Technical Physics, 2011, 56:11, 1539–1545

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