Gibbs fluctuation theory in the context of electrochemical equilibrium noise

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.