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Based on the mean first passage time (MFPT) theory, we derive the expressionof the MFPT in the energy-diffusion controlled regime with a power-lawdistribution. We discuss the finite barrier effect (i.e. thermal energy is notsmall with respect to the potential barrier) and compare it with the Kramersinfinite barrier result both in the power-law distribution and in aMaxwell-Boltzmann distribution. It is shown that the MFPT with the power-lawdistribution extends the Kramers' low damping result to the relatively lowbarrier. We pay attention to the energy-diffusion controlled regime which is ofgreat interest in the context of Josephson junctions, and study how thepower-law parameter affects the current distribution function in the experimentof Josephson junctions.

The mean first passage time in an energy-diffusion controlled regime with power-law distributions