  Mesoscopic superconducting-normal-metal-superconducting (S-N-S) junctions
with a large separation between the superconducting electrodes (i.e. wide
junctions) exhibit nonequilibrium supercurrents, even at temperatures for which
the equilibrium Josephson effect is exponentially small. The second harmonic of
the Josephson frequency dominates these currents, as observed in recent
experiments. A simple description of these effects, in the spirit of the
Resistively-Shunted-Junction model, is suggested here. It is used to calculate
dc I-V characteristics, and to examine the effects of various types of noise
and of external microwave radiation (Shapiro steps). It is found that the
nonequilibrium supercurrents are excited when the junction is driven by a dc
bias or an ac bias, or even by external noise. In the case of junctions which
are also long in the direction perpendicular to the current flow, thermodynamic
phase fluctuations (thermal noise) alone can drive the quasiparticles out of
local equilibrium. Magnetic flux is then predicted to be trapped in units of
Phi_0 /2 = hc/4e.
