In a mesoscopic superconductor- normal metal - superconductor (SNS) he
terostructure the quasiparticle distribution can be driven far from eq
uilibrium by a voltage applied across the normal metal. This reduces t
he supercurrent between the superconducting electrodes, which creates
the possibility of using these SNS junctions as fast switches and tran
sistors. We describe the system in the framework of the quasiclassical
theory and find,good a,agreement with recent experiments. We propose
further experimental tests, for instance, the voltage dependence of th
e current-phase relation, which includes a transition to a pi junction
. [S0031-9007(98)06894-X].