The Einstein Fluctuation–Dissipation Relation as Applied to the Analysis of the Electrochemical Noise Resistance

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Abstract
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.

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