  In bulk systems the calculation of the main thermodynamic quantities leads to
the same expectation values in the thermodynamic limit, regardless of the
choice of the statistical ensemble. Single linear molecules can be still
regarded as statistical systems, where the thermodynamic limit is represented
by infinitely long chains. The question of equivalence between different
ensembles is not at all obvious and has been addressed in the literature, with
sometimes contradicting conclusions. We address this problem by studying the
scaling properties of the ensemble difference for two different chain models,
as a function of the degree of polymerization. By characterizing the scaling
behavior of the difference between the isotensional (Gibbs) and isometric
(Helmholtz) ensembles in the transition from the low-stretching to the
high-stretching regime, we show that ensemble equivalence cannot be reached for
macroscopic chains in the low force regime, and we characterize the transition
from the inequivalence to the equivalence regime.
