We present a theory for the nonequilibrium current in a mesoscopic Josephson junction which is coupled to a normal electron reservoir, and apply it to a chaotic junction. Large sample-to-sample fluctuations of the critical current $I_{ \rm c}$ are found, with ${ rms} I_{ \rm c} \simeq \sqrt{ N}e\Delta/\hbar$, when the voltage difference eV between the electron reservoir and the junction exceeds the superconducting gap $\Delta$ and the number of modes N connecting the junction to the superconducting electrodes is large.
Categories: cond-mat.supr-con
