  The distinctive quasiparticle distribution existing under nonequilibrium in a
superconductor-insulator-normal metal-insulator-superconductor (SINIS)
mesoscopic line is proposed as a novel tool to control the supercurrent
intensity in a long Josephson weak link. We present a description of this
system in the framework of the diffusive-limit quasiclassical Green-function
theory and take into account the effects of inelastic scattering with arbitrary
strength. Supercurrent enhancement and suppression, including a marked
transition to a $\pi$-junction are striking features leading to a fully tunable
structure. The role of the degree of nonequilibrium, temperature, and materials
choice as well as features like noise, switching time, and current and power
gain are also addressed.
