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We model the normal resistance of a hysteretic Josephson junction by writing a master equation to describe the individual quasiparticle tunneling. We solve the master equation by a WKB method near the zero-voltage state and near the nonzero-voltage state. We find that near the zero-voltage state the solution is given by the Boltzmann distribution with second-order corrections while near the nonzero-voltage state we obtain a nonsymmetric, non-Boltzmann distribution of voltage fluctuations, similar to the results obtained in a previous discussion based on the Fokker-Planck equation.
Ben‐Jacob et al. (1986) studied this question.