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

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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.

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Authors and Affiliations

  1. Institute of Thermal Physics, Ural Branch, Russian Academy of Sciences, ul. Amundsena 106, Yekaterinburg, 620016, Russia

    V. P. Koverda & V. N. Skokov

Authors
  1. V. P. Koverda
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  2. V. N. Skokov
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Correspondence to V. P. Koverda.

Additional information

Original Russian Text © V.P. Koverda, V.N. Skokov, 2011, published in Zhurnal Tekhnicheskoi Fiziki, 2011, Vol. 81, No. 11, pp. 1–6.

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Koverda, V.P., Skokov, V.N. Entropy maximum in a nonlinear system with the 1/f fluctuation spectrum. Tech. Phys. 56, 1539–1545 (2011). https://doi.org/10.1134/S1063784211110156

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  • DOI: https://doi.org/10.1134/S1063784211110156

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