On the thermal fluctuations of free charge in the Ershler-Randles circuit

Noise method for the analyzing of thermodynamic second-order fluctuations of the electrical double layer charge in complicated electrochemical systems is developed. The method is based on the joint application of the Nyquist fluctuation-dissipation theorem and Laplace transform. Second-order fluctuations of the free charge in the electrical double layer are studied under the conditions when the weak-signal faradaic impedance of equilibrated electrode is determined by the diffusion impedance, alongside with the slow-discharge resistance. It is shown that, unlike the high-order fluctuations, the level of thermodynamic second-order fluctuations of the free charge does not depend on the mechanism of interaction of the thermodynamic system with thermostat; it fully corresponds to the conceptions of the Gibbs statistical thermodynamics.