Abstract: A stochastic theory of non-equilibrium thermodynamics of time-dependent potentiostatic D.M.E. processes was established in this paper. Based on a simplified stochastic model of non-steady state irreversible electrode processes the quantitative analysis of both the fluctuations and dissipation in this kind of important physico-chemical systems becomes possible. By means of it, we introduce successfully the basic stochastic formula of non-equilibrium thermodynamics of the potentiostatic DME(dropping mercury electrode) processes as well as a stochastic algorithm useful for theoretical deduction of the polarogram curve. Furthermore, in a limit case of the slow growth of the drop for the DME process with very hesitative diffusion steps(Ψ_EC→0) the polarogram equation induced by the fluctuations is derived under the quasi-steady state approximation. The result corroborates the polarogram equation from Nernst formula in the near equilibrium region. As a typical illustration, an example is given to calculate the deviation of polarogram curve induced by the fluctuations. Under the condition that the asymptotic form of probability distribution is established on the basis of the central limit theorem, the deviation of the current becomes the largest with the potential close to the half-wave potential. This means the fluctuations have great influence on the half-wave potential with very hesitative diffusion steps.

Key words: Stochastic theory of non-equilibrium thermodynamics, Time-dependent process, Fluctuations-dissipation, Dropping mercury electrode(DME) processes