Theory of asymmetric electrochemical stochastic diffusion

Strict analysis of electrochemical strochastic diffusion due to asymmetric Brownian motion of electric charge in an equilibrium electrochemical ac circuit containing double electric layer capacitance and noisy Faradaic resistance is carried out. Cumulant analogs (for 3rd and 5th order correlations) of the Einstein formula are obtained. It is proved that equilibrium asymmetric (nongauss) stochastic diffusion is in agreement with the central limiting theorem of the probability theory. The Hurst exponent was found in the case of the nongauss components of the process of equilibrium stochastic diffusion. Apart from electrochemistry, the performed stochastic analysis of equilibrium electrochemical nongauss diffusion is also of general theoretical interest, including its application in the stochastic theory of asymmetric anomalous transport and strict theory of fluctuations at large deviations from equilibrium.