Journal of Biological Physics

, Volume 38, Issue 2, pp 201–207

Hill’s small systems nanothermodynamics: a simple macromolecular partition problem with a statistical perspective

Short Note


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 system size-dependent equilibrium constant for the bulk-membrane partition, we obtain Hill’s results on differential and integral chemical potentials μ 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 the system’s size; it is closely related to the system’s fluctuations and inhomogeneity. These results provide a better understanding of nanothermodynamics and clarify its logical relation with the theory of statistical mechanics.


Nanothermodynamics Ensemble Fluctuation Small systems  Statistical mechanics 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

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