  Recent formation and structure models of Jupiter suggest that the planet can
have composition gradients and not be fully convective (adiabatic). This
possibility directly affects our understanding of Jupiter's bulk composition
and origin. In this Letter we present Jupiter's evolution with a primordial
structure consisting of a relatively steep heavy-element gradient of 40 Earth
masses. We show that for a primordial structure with composition gradients,
most of the mixing occurs in the outer part of the gradient during the early
evolution (several 10^7 years), leading to an adiabatic outer envelope (60% of
Jupiter's mass). We find that the composition gradient in the deep interior
persists, suggesting that about 40% of Jupiter's mass can be non-adiabatic with
a higher temperature than the one derived from Jupiter's atmospheric
properties. The region that can potentially develop layered-convection in
Jupiter today is estimated to be limited to about 10% of the mass.
