Physics of free climbing

The theory of stochastic processes provides theoretical tools which can be efficiently used to explore the properties of noise-induced escape kinetics. Since noise-facilitated escape over the potential barrier resembles free climbing, one can use the first-passage time theory in an analysis of rock climbing. We perform the analysis of the mean first-passage time in order to answer the question regarding the optimal, i.e., resulting in the fastest climbing, rope length. It is demonstrated that there is a discrete set of favorable rope lengths assuring the shortest climbing times, as they correspond to local minima of mean first-passage time. Within the set of favorable rope lengths there is the optimal rope giving rise to the shortest climbing time. In particular, more experienced climbers can decrease their climbing time by using longer ropes.