  Using a simple example of biological macromolecules which are partitioned
between bulk solution and membrane, we investigate T.L. Hill's phenomenological
nanothermodynamics for small systems. By introducing a {\em systems size
dependent} equilibrium constant for the bulk-membrane partition, we obtain
Hill's results on differential and integral chemical potentials $\mu$ and
$\hat{\mu}$ from computations based on standard Gibbsian equilibrium
statistical mechanics. It is shown that their difference can be understood from
an equilibrium re-partitioning between bulk and membrane fractions upon a
change in system's size; it is closely related to the system's fluctuations and
inhomogeneity. These results provide a better understanding of the
nanothermodynamics and clarify its logical relation with the theory of
statistical mechanics.
