  Theories that are used to extract energy-landscape information from
single-molecule pulling experiments in biophysics are all invariably based on
Kramers' theory of thermally-activated escape rate from a potential well. As is
well known, this theory recovers the Arrhenius dependence of the rate on the
barrier energy, and crucially relies on the assumption that the barrier energy
is much larger than $k_{B}T$ (limit of comparatively low thermal fluctuations).
As was already shown in Dudko, Hummer, Szabo Phys. Rev. Lett. (2006), this
approach leads to the unphysical prediction of dissociation time increasing
with decreasing binding energy when the latter is lowered to values comparable
to $k_{B}T$ (limit of large thermal fluctuations). We propose a new theoretical
framework (fully supported by numerical simulations) which amends Kramers'
theory in this limit, and use it to extract the dissociation rate from
single-molecule experiments where now predictions are physically meaningful and
in agreement with simulations over the whole range of applied forces (binding
energies). These results are expected to be relevant for a large number of
experimental settings in single-molecule biophysics.
