  Single-molecule stretching experiments are widely utilized within the fields
of physics and chemistry to characterize the mechanics of individual bonds or
molecules, as well as chemical reactions. Analytic relations describing these
experiments are valuable, and these relations can be obtained through the
statistical thermodynamics of idealized model systems representing the
experiments. Since the specific thermodynamic ensembles manifested by the
experiments affect the outcome, primarily for small molecules, the stretching
device must be included in the idealized model system. Though the model for the
stretched molecule might be exactly solvable, including the device in the model
often prevents analytic solutions. In the limit of large or small device
stiffness, the isometric or isotensional ensembles can provide effective
approximations, but the device effects are missing. Here, a dual set of
asymptotically correct statistical thermodynamic theories are applied to
develop accurate approximations for the full model system that includes both
the molecule and the device. The asymptotic theories are first demonstrated to
be accurate using the freely jointed chain model, and then using molecular
dynamics calculations of a single polyethylene chain.
