The second Gibbs paradox

Gibbs's article "On the Equilibrium of Heterogeneous Substance" is sometimes hard to read. As a consequence, some of his more surprising statements are not widely known. I will focus on what Gibbs wrote about the equilibrium between a small crystallite and a fluid, namely that for small crystallites, the chemical potential of the solid at the pressure and temperature inside the crystallite need not be equal to the chemical potential of the liquid with which it is in equilibrium. Surely, that cannot be true ... or can it? I will try to explain.