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

TL;DR

This paper explores Hill's nanothermodynamics for small biological systems by linking it to statistical mechanics, demonstrating how system size affects chemical potentials and fluctuations in macromolecular partitioning.

Contribution

It introduces a size-dependent equilibrium constant to connect Hill's nanothermodynamics with standard statistical mechanics, clarifying their relationship.

Findings

Differential and integral chemical potentials derived from statistical mechanics.

Difference between chemical potentials explained by system size re-partitioning.

Results enhance understanding of nanothermodynamics and its statistical basis.

Abstract

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.