The statistical mechanics and the thermodynamics of small systems are characterized by 1 the non-equivalence of the statistical ensembles. Concerning a polymer chain or an arbitrary chain 2 of independent units, this concept leads to different force-extension responses for the isotensional 3 (Gibbs) and the isometric (Helmholtz) thermodynamic ensembles for a limited number of units 4 (far from the thermodynamic limit). While the average force-extension response has been largely 5 investigated in both Gibbs and Helmholtz ensembles, the full statistical characterization of this 6 thermo-mechanical behavior has not been approached by evaluating the corresponding probability 7 densities. Therefore, we elaborate in this paper a technique for obtaining the probability density of the 8 extension when the force is applied (Gibbs ensemble) and the probability density of the force when the 9 extension is prescribed (Helmholtz ensemble). This methodology, here developed at thermodynamic 10 equilibrium, is applied to a specific chain composed of units characterized by a bistable potential 11 energy, which is able to mimic the folding and unfolding of several macromolecules of biological 12 origin. 13