Inequivalence of Statistical Ensembles in Single Molecule Measurements

TL;DR

This paper investigates the differences between statistical ensembles in single molecule force measurements, highlighting ensemble inequivalence and its implications for interpreting experimental data.

Contribution

It introduces the concept of ensemble inequivalence in single molecule experiments using the WLC model and discusses the importance of transition free energy in ensemble transformations.

Findings

Ensemble inequivalence affects force-extension measurements.

Rigid rod limit illustrates the inequivalence clearly.

Non-monotonic force-extension curves are ruled out in some ensembles.

Abstract

We study the role of fluctuations in single molecule experimental measurements of force-extension curves. We use the Worm Like Chain (WLC) model to bring out the connection between the Helmholtz ensemble characterized by the Free Energy and the Gibbs ensemble characterized by the Free Energy . We consider the rigid rod limit of the WLC model as an instructive special case to bring out the issue of ensemble inequivalence. We point out the need for taking into account the free energy of transition when one goes from one ensemble to another. We also comment on the ``phase transition'' noticed in an isometric setup for semiflexible polymers and propose a realization of its thermodynamic limit. We present general arguments which rule out non-monotonic force-extension curves in some ensembles and note that these do not apply to the isometric ensemble.