  Unlike fluids at thermal equilibrium, biomolecular mixtures in living systems
can sustain nonequilibrium steady states, in which active processes modify the
conformational states of the constituent molecules. Despite qualitative
similarities between liquid--liquid phase separation in these systems, the
extent to which the phase-separation kinetics differ remains unclear. Here we
show that inhomogeneous chemical reactions can alter the nucleation kinetics of
liquid--liquid phase separation in a manner that is consistent with classical
nucleation theory, but can only be rationalized by introducing a nonequilibrium
interfacial tension. We identify conditions under which nucleation can be
accelerated without changing the energetics or supersaturation, thus breaking
the correlation between fast nucleation and strong driving forces that is
typical of phase separation and self-assembly at thermal equilibrium.
