A generalized stochastic model of the irreversible electrode processes is proposed. By means of it the dissipation and the fluctuation around nonequilibrium steady states of the electrode chemical reaction systems is analyzed. It is shown that the polarizations, in spite of the concentration polarization or the electrochemical polarization, originate from the nontrivial dissipations together with the non-Poissonian fluctuations in irreversible electrode processes. Furthermore a dissipation-fluctuation formula of electrode polarization is deduced explicitly. This formula is a dominant nonequilibrium thermodynamic equality, useful for the theoretic analysis of the polarization in irreversible electrode processes when the validity of the classical equilibrium thermodynamics breaks down. It turns out that the well-known Nernst formula followed by concentration polarization and the famous Tafel equation valid for electrochemical polarization are only the macroscopic approximations of two special limit cases in the formalism presented in this paper. If the fluctuation departs from the Gaussian a revision will be inevitable.