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We present a theory for the nonequilibrium current in a mesoscopic Josephsonjunction which is coupled to a normal electron reservoir, and apply it to achaotic 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 junctionexceeds the superconducting gap $\Delta$ and the number of modes N connectingthe junction to the superconducting electrodes is large.Comment: 4 pages, 3 figure

Large sample-to-sample fluctuations of the nonequilibrium critical current through mesoscopic Josephson junctions