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

Hill's Small Systems Nanothermodynamics: A Simple Macromolecular Partition Problem with a Statistical Perspective