Boris M. Grafov

Within the framework of the Einstein fluctuation–dissipation relation, the theoretical analysis of the noise resistance is carried out for two classical electrochemical ac circuits: Ershler–Randles and Frumkin–Melik-Gaikazyan. It is shown that as the sampling period of the noise signal increases, the noise resistance in the Ershler–Randles circuit tends to its limiting value which coincides with the slow discharge resistance. The asymptotic behavior of the Frumkin–Melik-Gaikazyan circuit is of a different manner. As the sampling period of the noise signal increases, the curve of the noise resistance of the Frumkin–Melik-Gaikazyan circuit transforms into a straight line with the tangent inversely proportional to the thermodynamic capacitance of the electrode. The fluctuation–dissipation relation of Einstein may be used in the theoretical analysis of the noise resistance of other electrochemical ac circuits.

The technique of Chebyshev polynomials of discrete variable is used to analyze a random time series. The main result of the work is a new theoretical relationship between the structure function and the discrete Chebyshev spectrum. The relationship is used for the trend-resistant structural analysis of electrochemical noise of corrosion process and for the trend-resistant structural analysis of electronic noise of measuring instrument. Not only the structure function of the analyzed random series, but also the structure function of trend is estimated. The theoretical relationship between the structure function and the discrete Chebyshev spectrum can be used for the trend-resistant structural analysis of random time series of any nature.

The ergodicity of electrochemical noise of corrosion process with respect to the three-dimensional Chebyshev spectrum is studied. The electrochemical noise of “two identical electrodes of...

The electrochemical noise verification of the Gibbs fluctuation theory shows that the Gibbs ergodic idea works perfectly with respect to the pair correlations of the electrode charge thermal fluctuations. At the same time, the Gibbs formulae for the triple- and higher-order correlations of the electrode charge thermal fluctuations are outside of the ergodic hypothesis. This failure of the Gibbs ergodic idea suggests that the noise version of the electrochemical charge-transfer theory should be developed. In the context of nano-electrochemistry, the second- and higher-order correlations of the electrochemical noise processes may be considered as the quantities suitable for the nano-electrochemical characterization of both the electrode processes and electrochemical devices.