  Theories of phase change and self-assembly often invoke the idea of a
`quasiequilibrium', a regime in which the nonequilibrium association of
building blocks results nonetheless in a structure whose properties are
determined solely by an underlying free energy landscape. Here we study a
prototypical example of multicomponent self-assembly, a one-dimensional fiber
grown from red and blue blocks. If the equilibrium structure possesses
compositional correlations different from those characteristic of random
mixing, then it cannot be generated without error at any finite growth rate:
there is no quasiequilibrium regime. However, by exploiting dynamic scaling,
structures characteristic of equilibrium at one point in phase space can be
generated, without error, arbitrarily far from equilibrium. Our results thus
suggest a `nonperturbative' strategy for multicomponent self-assembly in which
the target structure is, by design, not the equilibrium one.
