Response to “Comment on ‘Elasticity of flexible and semiflexible polymers with extensible bonds in the Gibbs and Helmholtz ensembles”’ [J. Chem. Phys. 138, 157101 (2013)

Abstract

Two different statistical ensembles can be considered for extending a single polymer chain: the Gibbs (or isotensional) ensemble characterized by a deterministic force applied to the free end of the chain (the other being fixed in a given reference frame), and the Helmholtz (or isometric) ensemble obtained with both the ends of the polymers tethered at two different points of the space. When the thermodynamic limit is satisfied (the number of monomers approaches infinity) these ensembles are equivalent from the thermodynamic point of view: it means that the constitutive equations (vector force-extension relations) assume the same mathematical form in both isotensional and isometric conditions. Equivalently, the Helmholtz and Gibbs free energies are linked by a Legendre transform. We explain that this general result is coherent with some “forms of inequivalence” observed by defining different average values of force and position vectors. However, this fact does not indicate thermodynamic inequivalence as largely discussed in the present Response.