  We consider the thermodynamic behavior of local fluctuations occurring in a
stable or metastable bulk phase. For a system with three or more phases, a
simple analysis based on classical nucleation theory predicts that small
fluctuations always resemble the phase having the lowest surface tension with
the surrounding bulk phase, regardless of the relative chemical potentials of
the phases. We also identify the conditions at which a fluctuation may convert
to a different phase as its size increases, referred to here as a "fluctuation
phase transition" (FPT). We demonstrate these phenonena in simulations of a two
dimensional lattice model by evaluating the free energy surface that describes
the thermodynamic properties of a fluctuation as a function of its size and
phase composition. We show that a FPT can occur in the fluctuations of either a
stable or metastable bulk phase and that the transition is first-order. We also
find that the FPT is bracketed by well-defined spinodals, which place limits on
the size of fluctuations of distinct phases. Furthermore, when the FPT occurs
in a metastable bulk phase, we show that the superposition of the FPT on the
nucleation process results in two-step nucleation (TSN). We identify distinct
regimes of TSN based on the nucleation pathway in the free energy surface, and
correlate these regimes to the phase diagram of the bulk system. Our results
clarify the origin of TSN, and elucidate a wide variety of phenomena associated
with TSN, including the Ostwald step rule.
